To solve this problem, we first need to simplify the given equation:

(a - b) / a = 4

Multiplying both sides by a:

a - b = 4a

Adding b to both sides:

a = 4a + b

Subtracting 4a from both sides:

-3a = b

Now we can substitute -3a for b in the expression (6a + 5b) / b:

(6a + 5(-3a)) / (-3a)

Simplifying further:

(6a - 15a) / (-3a)

-9a / -3a

-3

Therefore, (6a + 5b) / b = -3.