Let the edges of the rectangular parallelepiped be a, b and c.

The diagonals of the three faces meeting at one corner are:

√(a² + b²) = √5
√(b² + c²) = √10
√(c² + a²) = √13

Squaring:

a² + b² = 5
b² + c² = 10
c² + a² = 13

Adding all three equations:

2(a² + b² + c²) = 5 + 10 + 13
2(a² + b² + c²) = 28

a² + b² + c² = 14

Now subtract:

(a² + b² + c²) − (a² + b²) = 14 − 5
c² = 9 → c = 3

Similarly,

(a² + b² + c²) − (b² + c²) = 14 − 10
a² = 4 → a = 2

(a² + b² + c²) − (c² + a²) = 14 − 13
b² = 1 → b = 1

Volume = a × b × c
= 2 × 1 × 3
= 6 cm³