In order to divide these polynomials, let's do the following steps:
15x³ divided by 5x: 3x²
3x² times (5x + 1): 15x³ + 3x²
15x³ + 13x² + 22x + 9 minus (15x³ + 3x²): 10x² + 22x + 9
10x² divided by 5x: 2x
2x times (5x + 1): 10x² + 2x
10x² + 22x + 9 minus (10x² + 2x): 20x + 9
20x divided by 5x: 4
4 times (5x + 1): 20x + 4
20x + 9 minus (20x + 4): 5
Therefore the quotient is 3x² + 2x + 4 and the remainder is 5.