forgot how to do it, brains have gone to after the summer holiday;
collect the like terms;
x^{2 }- 4ax - 5a^{2 }= (x+a)(x-5a), not sure how to get there though, probably completing the square
For any polynomial p(x), if you can find a root r, so p(r) = 0, then (x-r) divides p(x) with remainder 0. so you get p(x) = (x-r)*quotient .
but in your case using the quadratic formula can also solve this dilemna.
So for the quadratic formula which gives roots so (x--a)*(x-5a) also gives you the factorization.