My experience of 5e, such as it is, has not illustrated that the combat system is particularly interesting, and can in fact get quite boring. People frequently tout the speed of combats, but I have yet to see a 5e combat run meaningfully faster
Speed is what saves it from being as boring as you might expect just from looking at the relative lack of options. And, you really should be seeing that difference, because it's prettymuch hardwired in. Attacks hit more often, saves fail more often, damage is higher, spells more powerful, and hps, at low level, anyway, are a lot lower. A turn may or may not go faster depending on who's taking it with what character under what circumstances, but there should simply be fewer rounds in most combats.
And, despite having taken community advice on the kind of character to play as a 4e-fan+5e-skeptic trying to give 5e a chance, I still feel like I have far too few choices.
Obviously, you should be playing a full caster. How short of choices can you feel with a character who chooses mod+3 dailies to 'know' vs at most 2 or 3 and casts 2 or 3 three of them vs 1, while still getting multiple at-wills? You still get to choose a Background, too. And, though you don't get a feat at 1st level, you aren't paying any 'feat taxes,' either. It seems like, as long as you want to play the right concept, you have a lot of choice relative to 4e. Nothing like 3.5, but that's not where you're coming from.
We've only gotten up to level 3, but combats are still mostly meat-grinder-y, leaving me terrified for my character's survival--a non-ideal situation when I'd specifically made the character for being decent-to-good at melee
By 3rd that should really be tapering off noticeably. Give it to 5th, if you don't see a complete turn-around by then, something's wrong.
But you do bring up one way that 5e combats can drag on a bit - and it's familiar to the point of nostalgic to those of us who played AD&D. 1st level characters are so fragile, and the new backgrounds/traits so encourage players to invest in their characters, that just letting them die like flies doesn't sit well with every DM. You can't just dial down encounters to the point their 'safe,' that'd not just be comical, it'd give far too little experience. What 5e does leave wide-open is 'ruling' in favor of the PCs' survival ('fudging') and that can make a combat that should have ended swiftly in a TPK drag on quite a bit.
I habitually describe my character's actions, so there's no improvement to be gained there, though I'm afraid I'm not quite clever/funny enough to come up with real zingers for vicious mockery every turn. Which, incidentally, vicious mockery the vast majority of what I do, because I have so few spells to work with, I feel compelled to hoard them until they're truly needed--mostly cure wounds, or the occasional faerie fire.
My players had a lot of fun with vicious mockery - it probably accounted for most of the mechanically-inspired fun they had, at 1st level, now that I think of it. But, yeah, focusing on the responsibility of the band-aid role will not provide you with a lot of fun. Cast spells like you would dailies in 4e if you had that many of them: whenever they'd be particularly helpful. Use Cure Wounds only if getting someone back up is critically important at that moment. Not only will it leave you more actions to have fun with, it'll run the party out of hps faster, so they'll rest sooner, and you'll re-charge your dailies.
The most frustrating thing is that I feel like I am supposed to have a substantial toolbox and lots of bells and whistles, but I'm either too terrified to use them, or can't justify the expenditure on so few threats (or so small a threat). For example, I'm playing a Dragonborn, but I have yet to use my dragon breath--because the only fight I've been in where it would've been worth using, I was bleeding on the floor by the end of the first round and never got the chance. I have allegedly powerful utility spells like sleep, but they succeed so rarely or so minimally, I can't justify spending the slot when it could instead be used to keep one of my allies from getting pasted.
You're definitely not managing your slots optimally. Healing is best used to bring an ally up from zero, when their next potential action after you revive them will be vital to the party's success. Anything less than that, and you can probably find a better use for the slot.
I don't dare get in melee range most of the time, because almost every time I have, I've been brutally punished for it
That's fine, casters are supposed to be melee-shy.
Yeah, I can definitely agree with that. It's one of D&D's numerous "chicken-and-egg" problems, and also one of its "all solutions MUST be extreme"* problems, unfortunately. (Really, it's "all solutions in the past have been extreme, so an edition which mainly prioritizes dressing up traditional mores must follow suit." But that's not as pithy.)
Not sure I follow the parenthetical, there...
I...find the second option you suggest hard to comprehend. What does the events during other peoples' turns matter, for my enjoyment of what I'm doing? Whether or not the things they do are interesting/dangerous/boring is...entirely orthogonal to whether I am turned off by the combat
Staying engaged includes staying interested in the whole battle, including what everyone else is doing. Though some groups can handle just playing on their turns, that's usually what gives a player a sense of combat being 'slow' or 'boring' (that and having to wait longer for their turn because everyone is having an individually-interesting turn). If you can enjoy the whole game, not just your 1/4th or 6th slice of it, it's less boring. In 5e, party composition matters. If you're all playing complex 'interesting' casters there'll be more time between your turns, if you've got some quick-turn classes in there, you get a larger share of play time in proportion to them.
It has been difficult for me. The CRs aren't much help. Some high CR creatures are pushovers, some lower CR creatures very tough. Encounter guidelines in the DMG aren't very helpful.
Coming from 3.5, you should be accustomed to compensating for comparatively rough CR guidelines. The key is not to trust them, and to go ahead and adjust on the fly, since no amount of pre-planning is going to be perfect. 5e frees you to do that, since it seems to have effectively undercut the Cult of RAW that gripped the 3e-era community.
Getting the right level of challenge has been difficult in this edition since monsters seem to fall into the too weak to too deadly category that doesn't seem to have a great deal to do with CR.
It is, indeed, like the olden days. More a matter of feel than numbers.
It's a failure for anyone that wants to model a grittier wound system. That's why it's always required optional rules to incorporate those concepts. I don't think hit points model 'plot armor.'
Then they've always been a failure, for you, of course.
I'd love to see those numbers, but I imagine no way to get them other than memory.
iserith is very much a storyteller, I doubt he has any entirely-un-planned deaths in his campaigns, and don't doubt that the body count is little-impacted by edition. 5e certainly gives a DM more lattitude to play in that style than 3.5 did, or rather, community attitude now vs then, thus.
In 1E and 2E getting snuffed was one missed saving throw away.
In 5E past the low levels, say 1-4 or 5, death is rather rare so far.
Of course, in 1e, saves got genuinely easier as you leveled up.
Unfortunately, our DM is big on playing RAW and without any frilly/extra rules, in part because he's somewhat new to 5e. That's the main reason why we started at level 1, for example. (Some of our players being new to TTRPGs in general also factored into that choice.)
Ooch. Not a great choice. Level 1 is really, strangely, not for beginners - it's where the game is tough/gritty/deadly/frustrating or however you want to couch it. Level 3 is a better place to start all around. A little overwhelming to jump into a full caster at 3rd, maybe, but there are a few simpler (sub-)class choices.
And playing RAW 5e is almost a contradiction in terms. The RAW tells the DM to ditch the RAW and make rulings, instead.
Also, part of the reason for our combats being so meat-grinder-y is that his other 5e group regularly punches well above its weight, while ours struggles to punch at weight. Game's currently on hiatus for the holidays, but he has repeatedly expressed his dismay at our group being unexpectedly easy to overwhelm. Thus far, his efforts to adjust have not quite felt effective, but it might be a problem of perspective for me.
5e really did 'Empower' the DM, but that does mean that the success/failure/excitement of the play experience is more on his shoulders than the system's. FWIW.