The sum of the square of a positive number and the square of 5 more than the number is 37. what is the number?

Writing this info out symbolically:

x^2 + (x+5)^2 = 37
Expanding, x^2+x^2+10x +25=37, or 2x^2+10x-12=0.
Reducing, x^2+5x-6=0.  factoring, (x-1)(x+6)=0
Solving for x:  x-1=0 results in x=1; x=6=0 results in x=-6.

We want only a positive result, so choose x=1 and discard x=-6.