Answer:
(x³ + bx² - 7x + 9)(x² + ax + 5) =
x⁵ + 13x⁴ + 38x³ - 22x² + 37x + 45
x⁵ + ax⁴ + 5x³ + bx⁴ + abx³ + 5bx² - 7x³
- 7ax² - 35x + 9x² + 9ax + 45 =
x⁵ + (a + b)x⁴ + (ab - 2)x³ + (-7a + 5b + 9)x²
+ (9a - 35)x + 45
9a - 35 = 37
9a = 72, so a = 8.
8 + b = 13, so b = 5.