$5$ in high and wide, and $10$ in long.
Work Step by Step
Let $x$ be the height and the width; then the length is $x+5$. Then our equation is: $x\cdot x\cdot (x+5)=250\\x^3+5x^2-250=0\\(x-5)(x^2+10x+5)=0$ The second term in the product has a positive discriminant, thus it cannot be $0$. Thus $x-5=0\\x=5$. Thus the prism is $5$ inches high and wide, and $10$ in long.