Is 5 > x > 0 ?

(1) x is an integer greater than 4.
(2) 5x² - 25x > 0

the question asks if x > 5, it could also EQUAL 5 with the first statement? In which case it would NOT BE GREATER THAN 5

The problem states that x is an integer. If it is bigger than 4 it can in fact be equal to 5, the question however asks us whether it can actually be smaller than 5. This is impossible, since x is at least 5.

I think you confused your inequality signs. We aren't asked if x is greater than 5, we are asked if its less than 5.