It is very backwards-looking, for the most part, but it does take a new spin, or a slightly more formal/different approach to a few things here and there. The well-liked Advantage/Disadvantage mechanics were present in 4e, as was the consolidation of 3.x's myriad bonuses & loss-of-DEX-bonus mechanics down to 'Combat Advantage.' Nothing new in that sense, but 5e further consolidated those mechanics & bonuses into Advantage, and did the same for penalties with Disadvantage. Similarly, PCs have been doing things when not adventuring, presumably, from the very beginning, and plenty of games have formalized that, or parts of that - 3e did for a few specific things like crafting or spell research, just as 1e had (crafting magic items, anyway) - but 5e's formalization of it as a named resource was "newish" to D&D, even as it happily evoked the feel of the classic game.
PF & 5e are both very backwards-looking projects, they cleave closely to a prior edition of D&D (3.5 and AD&D, respectively) in many ways, and are committed to evoking them. PF cleaves closer in mechanics and player-side experience, 5e closer in softer measures like 'feel' and in DM 'empowerment,' but they're very much kindred spirits in that respect.
