Question

sqrt((sqrt(x2+66^2)+x)/x) - sqrt (x.sqrt(x2+66^2)-x2)=5

Answer 1

Really ?

fixing your sqrt and your x2 to x^2 as
√((√(x2+66^2)+x)/x) - √ (x√(x2+66^2)-x^2)=5

I sent it through Wolfram and they got

x = 6/√116

http://www.wolframalpha.com/input/?i=%E2%88%9A%28%28%E2%88%9A%28x2%2B66%5E2%29%2Bx%29%2Fx%29+-+%E2%88%9A+%28x%E2%88%9A%28x2%2B66%5E2%29-x%5E2%29%3D5

To actually do it, I would take the 2nd term to the right side, square both sides, simplify and probably square again.
Way too much typing for me on a Sunday morning.