The tricks you can do

Length of the median on the hypotenuse of a right angled triangle is always half the hypotenuse. Just think of Thales theorem!

i.e. the hypotenuse is the diameter of a circle, the median on the hypotenuse is the radius (from the center of the circle - MP of the hypotenuse - to the edge)

The midpoint of $AC$ is the circumcentre of $\triangle ABC$ . The length $BD$ is the radius of the circumcircle of ABC. The radius is also half the distance of AC which is half of 5, which is 2.5.

By Stewart's Theorem, we have that the length of the median $BD$ is:

$BD=\dfrac{\sqrt{2(a^2+b^2)-c^2}}{2}$

But this is a right triangle, so:

$BD=\dfrac{\sqrt{2c^2-c^2}}{2}=\dfrac{c}{2}$

We are given $c=5$ , so $BD=\boxed{2.5}$ .

Length of median drawn to side C can be represented by $\frac{\sqrt{2A^2+2B^2-C^2}}{2}$