There are many similarities between Pathfinder D&D 5E. It is not only because they are both d20-based games but also of their shared heritage and analogous method of determining success. Having played through Hoard of the Dragon Queen and a good portion of The Rise of Tiamat, and given 5E’s very small product catalogue, there are a number of Paizo products that provide interesting options for gameplay and are also easily adaptable. This is especially so for Ultimate Campaign and here are a few elements that I think others might find particularly useful.
Traits & Drawbacks: One of the things I really enjoy about 5E are backgrounds, but what you might find is that in very tightly directed adventures, you may not be able to make use of the benefits that it provides. Traits offer a modest but not insignificant mechanical benefit that also adds to your character’s… well, character. If you want to go a step further, since backgrounds are not supposed to add a mechanic benefit, drawbacks can offset the bonus while accentuating your character flaws.
Story Feats: It may seem counter-intuitive, especially as much as feats have changed between the two games, but story feats can not only go toe-to-toe with those in the Player’s Handbook but provide game mechanics that both influences and is effected by the narrative being told at the table. The only drawback is that each has a certain event requirement before the full benefit of the feat is realized, but it can also be said that this provides player incentive to act in ways that move his or her character towards that goal.
Exploration & Kingdom Building: Kingmaker is an adventure path that I missed the boat on but have been really meaning to play or run and these rules are the ones I am most enthused about adding into 5E. The best thing about these two rulesets is that the mechanics do not effect other aspects of the game, but are affected by other aspects of the game, such as if your player invested heavy in Charisma. I would love to run a 5E game set in Chult, the Chondalwood, or some other hinterland in the Forgotten Realms, where the players are discovering the secrets of the landscape and effects of the Sundering.