In order to factorize the given expression, we find to find two numbers p and q such that:

p + q = 5, pq = -36

Clearly,

9 – 4 = 5, 9 (-4) = -36

Therefore, split 5y as 9y – 4y

Therefore,

y² + 5y – 36 = y² + 9y – 4y – 36

= y (y + 9) – 4 (y + 9)

= (y – 4) (y + 9)