If x and y are integers, then the equation 5x + 19y = 64 has
5x + 19y = 64
If y = 1, there is an integer solution for x = 9, now if y changes (increases or decreases) by 5, then x will change (decrease or increase) by 19.
Looking at the options, if x = 256, you get y = 64.
So, there is a solution for 250 < x < 300.
The correct option is C.