The engine may very well come into use when resolving things like how to get past that red dragon--it probably involves skill checks, for example. But it may or may not involve use of limited resources like spell slots, so that may not have much effect on whether you're at peak operation.
(ETA) Imagine that the level 5 party is trying to get past the ancient red dragon. The bard gets a 23 on a Performance roll to enthrall the dragon with tales of how the party found a stash of more treasure than they could carry away, convincing the dragon that there's a huge pile of gold nearby just waiting to be added to its hoard. Meanwhile, the rogue gets a 27* on a Stealth check to sneak behind the dragon's back and steal the key to the Hidden Fortress of Marzuk without being noticed. The 5E mechanics were used, no limited resources were expended, the engine was not operating at its peak, and at the end of the evening, the players of those two characters feel awesome because they contributed to the session, even though the bard still has the majority of spell slots left when the PCs camp for the night.
*Roll of 17 on the die, 18 (+4) DEX, +3 proficiency bonus, Expertise in Stealth (so a +10 bonus in all). An ancient red dragon has a passive Perception of 26.