1000 Unsullied soldiers (commanded by Grey Worm), with their standard equipment, face off against 5000 wights (standard wights, no actual White Walkers or wight giants etc).
The fight takes place in an open field, starting distance of 50 yards, and will continue until the entirety of one of the armies is killed.
They're already up by 4000 over the Unsullied. Which means each warrior has to take out a whole bunch of wight's without getting hurt at all to feasibly win.
Also, Wights can't really be hurt, and can carry on after injuries. Even headshots don't always work unless you've got Dragonglass. Did you give them all Dragonglass shields and spears?
Lol Jon Snow and the others in season 7 killed dozens just themselves, and most of them just had normal weaponry. Also it's only 5-1 in the wights favor...which means that each Unsullied would have to defeat 5 wights for every one of them. Even if you still want to back the wights, I see no reason why it's unreasonably to think that the highly trained Unsullied soldiers could take at least a few of the wights individually themselves before falling.