Fermat's Last Theorem - Special Case of Sophie Germain Primes
These two cases are traditionally called ${\bf Case \,\, 1}$ and ${\bf Case \,\, 2}$, and you are after a proof of Case 2.
The essence of Dirichlet's proof of Case 2 when $p=5$ can be found in Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory, by Harold M. Edwards. It's in chapter three, at about page 70.