\sqrt{x+5}+\sqrt{20-x} =7

Square both sides of the equation,

x+5+2\sqrt{x+5}\sqrt{20-x}+20-x=49

\sqrt{x+5}\sqrt{20-x}=12

Square both sides of the equation again,

(x+5)(20-x) = 144

x^2-15x+44=0

Factoring the quadratic expression on left hand side

(x-4)(x-11)=0

Now we have found the solution for the equation.

x=4 or x=11