Yes, your character is basically unstoppable*
First, I'm going to assume that there is some sort of engine (extradimensional supercomputer, deity, alien, whater) which grants the powered individual this capability and interfaces directly with their brain (or soul depending on setting).
Secondly, I'm going to assume that whatever this Precognition Engine does isn't true precognition but rather simulated precognition. This means there's no actual time travel or future-observation going on, instead, the precognition engine is hooked up to some sort of panoptical system which is capable of viewing the users' entire (or even just local) reality at a particulate level (smaller or bigger adjust prediction accuracies). To "see" the future, the Engine performs simulations. This prevents nasty causality issues and the other weirdness that accompanies time travel.
Finally, I'm going to assume that the Engine is capable of precogging the power's user's brain, effectively granting meta-precognition. Otherwise, the user would only ever see one, rapidly shifiting future, since the Engine is capable of perfectly prediciting the future (in the short term).
Also, if your User has a gun, then they would be absolutely unstoppable.**
A simulated gunfight, from the precognative side:
The person who's connected to the Precognative Engine (the User) is of the opinion that they do not want to get shot. The Engine "knows" this (although it's not necessarily sentient).
Now, a gunman is approaching the user, and the Engine calculates that in five seconds, the gunman will have aimed, fired, and hit the User. Next, the Engine simulates what the User would choose to do when presented with this information, and the simulated User decides to, lets say, take a step to the left a second before the gun is fired. Simulating this course of action, the Engine discovers that the gunman is good enough to partially adjust their aim and the User get's winged on the arm instead. This data, is once again fed to the Engine's simulation of the User, which again "decides" to avoid this fate and chooses a different simulated action.
This simulate-query-resimulate loop continues onwards until the simulated User is presented with a satisfactory action, and this process works onwards continously.
The User, unaware of what's going on "behind the curtain" simply sees all the possible futures of the choices that simulated-User made and eventually settles on the same choice that simulated-User eventually made (free will is dead, but whatever). Then, they perform the exact set of actions that allow them to avoid getting shot.
The same gunfight, but from the gunman's perspective:
The gunman is a professional. They sight the User with their gun, line up a shot, and are about to press the trigger, when suddenly the User steps to the side a bit. The gunman readjusts their aim, but again, just before they're about to pull the trigger, the User is coincidentally not lined up properly anymore. Frustrated, they continue trying to get a bead on the User, but always just before they're about to fire the perfect shot, the User does something that makes them feel like they'd miss if they pulled the trigger. Eventually, the gunman can't take this anymore and losens their tolerances on what's an accepatable shot and starts shooting, even if they don't have a hit lined up. It dosen't help though, the User seemingly dances or limbos across the field of fire without getting hit once.
*There are scenarios where the User can get hit. Notably, they can get hit by area-affect weapons like bombs or grenades where they can't get out of the danger zone within five seconds (unless they can disable the bomb or grenade before it goes off, for example by shooting it or getting someone else to shoot it) or they can get hit by enough massed-fire, although it would take a serious amount of bullets to make it that there's no possible dodging window and the User would be stupid to put themselves in a situation like that. The most effective way to kill the User is to unknowingly poison them and then make sure they aren't in an enviroment where they can precognatively find the antidote or how to make an antidote in under 5 seconds.
**If the User has a gun, they basically become unstoppable. Then, they can do fancy things like:
- shoot opponents just right so they twitch and shoot their neighbors just right
- shoot bullets which ricochet just right and jams weapons
- shoot enemy vehicles just right so they get disabled instantly
- shoot bullets, grenades, etc out of the air with multiple ricochets
To highlight how ridiculously bullshit this power could be, imagine the user is in an empty field, with a gun, facing 12 professional soldiers. It's a standoff. Then, the User simply finds the future where shooting one of the soldiers just right makes them twitch their gun to the side and shoot 11 perfect, friendly-fire, headshots on their fellow squadmates before dying themselves. To see an example of what it could look like to watch a precognative fight, take a look at this clip where Bart disables all her opponents, even when starting from extreme disadvantage (although the power Bart has is slightly different) or take a look at Contessa in Wildbow's Worm (although her power is also slightly different).