Explanation

Sides other than hypotenuse of an isosceles triangle are equal.

Let the other two sides be $x$ each.

Using pythagoras theorem 

$$\begin{gathered} x^2+x^2={\left(5\sqrt{2}\right)}^2 \\ 2x^2=50 \\ \Rightarrow x^2=25 \\ \Rightarrow x=5cm \end{gathered}$$

So the other two sides are $5cm$ each.