Hiya!
As others have succinctly put it...5e is a great system, but you really need to give it a serious run before deciding what to pull from it (or use 5e outright instead). I bought the Starter Set and gave it a quick read and look-see. I wasn't sure about it at all...so it sat on my shelf for a month or two. Then, while waiting for other players to arrive, me and two players that were here decided to give it a shot until the others got here. The picked characters, and off we went.
Long story short...we three were stunned at how well it played and
felt. It just
felt like D&D. It didn't feel like a bunch of rules and 'options' in the guise of a "role playing game". It wasn't confusing as to what we needed to "do" to, er, "do" something in game. Simple language that was easy for me to interpret (e.g., "The character is better at detecting ambushes" vs "The character has +2 to Perception skill checks when in Hill or Mountain terrain and not wearing metal armor in order to detect ambushes"; I'll take the former
every day of the week, thank you very much!

). We started a 5e game two sessions later, shelving our current RPG campaign at the time. Now, your players may be all into the whole "micro transaction" play style of 3.x/PF/4e, which means they probably won't really grock the "macro choice" play style of 5e.
In 3.x, you get "6 skill points, one feat, choice of one of 19 classes, each that gives one to three sub abilities that interact with your other choices", so you can really customize the "numbers" of your character. It doesn't tell you much about your character other than "he now has +4 on Skill A in stead of +3", and a bunch of other 'abilities' that give minimal bonuses. The character concept that the player is going for isn't going to arrive for multiple levels...after getting enough skill points, feats and class abilities to make his "Skill roll, +8" noticable over everyone elses "Skill roll, +3".
In 5e, you get a "macro" feeling. Your character will "have Skill A as a Proficiency". Others don't. After gaining multiple levels and adventuring...your character still has Skill A, and others don't. Your overall, "macro Proficiency bonus" adds to your Skill A and not to anyone elses. Now, this is where 5e changes
significantly from 3.x;
The DM's input, use, and adjudication of ALL things...skill checks, ability checks, combat choices, spell results, etc...is NEEDED! A DM is
expected to use his/her own 'style' of DM'ing to make the game feel real and give players a good time. For me, I always give the character who has a skill, for example, more "knowledge" or a better "result" when succeeding on a check. So, if a Proficiency character is making a Perception roll, and so is everyone else who doesn't have Perception as a Proficiency...and everyone succeeds, I give the "notice" to the character with the skill, regardless of who rolled better (e.g, DC 10, Proficient character rolls an 11...everyone else succeeds and rolls 16's to 20's...I still indicate that the Proficient character "sees a slightly brighter shadow form in the back corner of the room, lurking next to the book case"). This gives players an incentive to "macro" their character in place of just trying to min/max the numbers. Having +8 on a skill because of a feat, min/maxed ability scores, and a class ability is still "less good" than having Proficiency in that skill.
I guess it boils down to this: In 5e, a player can play a character "concept" once he hits level three (and, btw, level 1 and 2 absolutely
zoom buy...as in two sessions you will be level 3; one session if it's a 8 hour one). In 3.x/PF, you frequently had to get a half-dozen levels, minimum, to really start to "feel" your character concept developing. As I said...5e, "macro" concepts...3.x/PF, "micro" concepts.
Sorry for the length. Bottom line...play 5e for three or four sessions. Then pick and choose what you want for your old game (or convert to 5e, like so many other 4e, PF, 3.x, 2e, 1e, and BECMI/RC folks have done).
^_^
Paul L. Ming