While I generally encourage doing your own thing rather than fan games in these sorts of scenarios then why not give it a try? Five Nights at Freddies (best if you note the game title just in case people are not familiar, or will not be familiar in a few years) is actually a fairly simple game underneath it all. Even more so if you build it up from the basic concept; however many rooms, a minor maze which is basically bridges problem setup in maths (plus contents only revealed by looking), the shutter power mechanic, timer, basic failure state (items in rooms move, if they move to/adjacent to an unshuttered main room then failure). Later "days" in the sequence might expand the AI from "moves randomly" to more predetermined paths, weighted movement towards player (distance to player = whatever, random move is weighted maybe 60/40 to moving towards player) or has awareness of power/camera state of player to make it harder, in addition to having more enemies in play.
The bulk of the game's general feel seems to be some pretty good art design and sound design, as well as at the time what was something of an inversion of the typical "I are powerful golden god" that was basically every game at some level, even those that pitched you as the underdog (see also glass cannon https://tvtropes.org/pmwiki/pmwiki.php/Main/GlassCannon ). If you are doing the usual fan game thing of "borrowing" art (which itself was also quite simple when it came down to it) then you are also somewhat spared that.