The fact that you have an isosceles triangle (two sides have the same length) makes this question easier that it might otherwise be. I drew your triangle ABC and joined the midpoint of the base D to the opposite vertex.
Triangles ABD and ADC are congruent and hence it follows that angle ADC is a right angle. Hence triangle ADB s a right triangle and thus by Pythagoras' Theorem
52 = 42 + h2
Solve for h.