3 feet tall
If it is in the shape of a tent and the floor is 8 feet across half of it cut down the middle would be 4 ft, you create a right triangle and can use the Pythagorean theorem to solve for the height. 5 is the hypotenuse and 4 is a leg.
a^2 + b^2 = c^2
Plug in the values known
4^2 +b^2 = 5^2
simplify
16+b^2=25
subtract 16 from both sides
b^2=9
take the square root of both sides
b=3 the hight is 3 ft