Since the only factors of 5 are 5 and 1, if the expression can be factored then the factored expression will have the form
(5x + a)(x + b)
Since the product of a and b is -18 the signs of a and must differ, one is positive and the other negative.
The factorizations of 18 are
1 18, 2 9, and 3 6
Now you need to go through the possibilities, one at a time, and see if you get a factorization of 5x2 - 27x - 18.
Try 1 and 18
(5x + 1)(x - 18)
(5x - 1)(x + 18)
(5x + 18)(x - 1)
(5x - 18)(x + 1)
Expand each. Do and of them give 5x2 - 27x - 18? If not try the next factorization of 18.