The Pythagorean theorem tells you the length of a face diagonal satisfies the relation
... (face diagonal)² = (5 in)² + (5 in)² = 50 in²
It also tells you the length of the space diagonal satisfies the relation
... (space diagonal)² = (5 in)² + (face diagonal)²
Substituting for the face diagonal term, we have
... (space diagonal)² = 25 in² + 50 in² = 75 in²
Taking the square root gives
... space diagonal = √(75 in²)
... space diagonal = 5√3 in ≈ 8.7 in