Question 827127
The length of each leg is {{{5sqrt(2)/2}}}{{{cm}}} .
That may be the expected answer.
You could also say that  one of the legs is the base, 
between angles measuring {{{90^o}}} and {{{45^o}}} ,
and the other leg is the height.
Then {{{base=hypotenuse*cos(45^o)}}} and {{{height=hypotenuse*sin(45^o)}}}
We know that {{{cos(45^o)=sqrt(2)/2}}} and {{{sin(45^o)=sqrt(2)/2}}} .
 
The length of the legs of the right isosceles triangle can also be calculated based on the Pythagorean theorem, without even mentioning trigonometric ratios.
If {{{x}}}{{{cm}}}= length of the legs of the right isosceles triangle,
according to the Pythagorean theorem,
{{{x^2+x^2=5^2}}}
{{{2x^2=5^2}}}
{{{x^2=5^2/2}}}
{{{x=sqrt(5^2/2)]]]
{{{x=sqrt(5^2)/sqrt(2)}}}
{{{x=5/sqrt(2)}}} , but since we do not like seeing square roots in denominators, we rationalize,
{{{x=5sqrt(2)/(sqrt(2)*sqrt(2))}}}
{{{x=5sqrt(2)/2}}}