Why does the model not move when 5 players are seated?

The issue here is that every loop, your code is appending all occupants to the Occupants table, but the table is never cleared. This means that the same occupant will appear multiple times in the table, and the table's length might never be 5. You want the end of your code to look like this:

	-- [snip]
	end
	wait()
	Occupants = {}
end

Perhaps more idiomatically, you could use a numerical value to count the occupants:

local part = game.Workspace.SpawnTruck
local ArmyTruck = game.Workspace.ArmyTruck
while true do
	local NumOccupants = 0
	for i,v in pairs(ArmyTruck:GetChildren()) do 
		if v:IsA("VehicleSeat") then
               		if v.Occupant ~= nil then
                    		NumOccupants = NumOccupants + 1
                	end
           	 end
        end

        print("There are "..NumOccupants.." on this army truck right now.")


	if NumOccupants == 5 then
		for i = 0,100,0.01 do
   			script.Parent:TranslateBy(Vector3.new(i,0,0))
    			wait(0.05)
		end
	end
	wait()
end