Let's break down the question an come up with parts of an equation that we can then put together to form a whole and solve.
Let 'a' be the number
So, 3 less than 5 times a number = 5a - 3
the number increased by 9 = a + 9
⇒The sum of 3 less than 5 times a number and the number increased by 9 is 24 ≡ (5a - 3) + (a + 9) = 24
⇒ (5a - 3) + (a + 9) = 24
⇒ 6a + 6 = 24
6a = 18
a = 3
∴ the number would be 3