The elevator starts at the main floor (which we can represent as 0), goes up 8 floors, and then goes back down 5 floors. To find its final position with respect to the main floor, we can simply add the upward movement and subtract the downward movement:
Final position = Starting position + Upward movement - Downward movement
Final position = 0 + 8 - 5
Final position = 8 - 5
Final position = 3
So, the integer that represents the elevator's final position with respect to the main floor is +3, meaning it is 3 floors above the main floor.