10ax-5ay+2bx-by

Factor first two terms: 10ax-5ay as 5a(2x-y)
Factor last two terms:  +2bx-by as +b(2x-y)

5a(2x-y)+b(2x-y)

Let U = (2x-y)

5aU+bU

U(5a+b)

Replace U by (2x-y)

(2x-y)(5a+b)

Edwin