Btw, is 5e really that much faster than 3e? Is it because of the more limited character creation options in the 5e test rules, lower levels in the playtest or is the system just faster? In other words, I am curious to what you think makes the system faster.
I don't believe that the options are "limited" in the test rules. I believe that all the options are in there already and anyone hoping that the final rules will be somehow more complex are fooling themselves.
But, yes, that's why it's faster. During a round of combat you have so few options that you come up with an action very quickly. You also don't have to worry about a bunch of rules that get in the way of resolving your action.
As an example:
3.5e: Alright, I move over here, by moving to this square, then this square, then this square, That provokes an attack of opportunity but I make a Tumble check DC 26 so I make it. Then I move to this square which provokes from this guy. He makes an attack roll and hits AC 28. That hits, I take 27 damage. Alright, now when I get to here I have flanking. I have a feat that allows me to add an extra d6 against targets I'm flanking. I'm then going to use another feat to use a level 5 spell to add +5 to hit and +5d4 points of damage to my next again. I then cast a swift action spell to make my attacks this round touch attacks. I then Power Attack for -10. I get to make my full round of attacks because I get pounce from this PrC here. Now, time to make my 5 attacks this round since I'm dual wielding and have improved two weapon fighting. Oh, that monster gets a free attack against me because I'm attacking his friend and he has a feat that lets him take an opportunity attack against someone who attacks his charge? Alright, he attacks me and hit AC 17 but misses. Back to my attacks. Attack #1...and so on.
5e: Hmm, I can...either make an attack or...no, that's my only real option. I make at attack against AC 19. I hit for 15 damage.
It's not just the amount of options, however. It's also the TYPE of options. Options that can be used to interrupt other people's turns take longer to resolve. Abilities that require specific activation and adding of numbers also take longer to resolve. A feat that permanently adds +2 to damage takes almost no time to resolve. An ability that allows you to use a spell slot to add +hit and +damage takes a while because now you have to consider whether you have the actions in a combat to use the feat, which spell slot you think you can lose without causing a problem, and whether it is worth it to add the extra damage.
With combats only lasting 10-30 minutes, you don't feel you are wasting time if you end up in a little fight. In 4e a random encounter can quickly take up the whole session if you have 2-3 hour sessions and a slow DM and a bazillion interrupts, minor actions, action points and conditions.
I admit that both in 2e when battles used to be very fast and in 5e sometimes minor battles can feel a little bit like a chore. The monsters aren't going to win and half the time they aren't even going to hit the PCs at all. Or if they do, they are going to cause so little damage that it isn't significant. However, the battles take so little time that I get over it very quickly and move on. Which is precisely why it feels more fulfilling. Sure, there was a kind of useless battle against skeletons in one room and zombies in another. However, during the session we managed to explore 15 rooms, find a bunch of treasure, defeat the lich ruling the complex, solve a riddle, and get past about 10 nasty traps. It feels like things get done.
Especially in contrast to some of my sessions in 3.5e or 4e. We'd literally fight 2 battles in a session. In between we would have opened one door.