To divide the polynomial (15 + 5x^2 - 3x^3 - 9x) by (5 - 3x), we can use long division.

First, let's set up the division:

-3x^2 + 2x + 3
_______________________
5 - 3x | -3x^3 + 5x^2 - 9x + 15

Now, let's divide the first term of the dividend by the first term of the divisor:

-3x^3 / -3x = x^2

Next, multiply the divisor (5 - 3x) by the quotient (x^2):

x^2 * (5 - 3x) = 5x^2 - 3x^3

Subtract this product from the dividend:

-3x^3 + 5x^2 - 9x + 15 - (5x^2 - 3x^3) = -3x^3 + 5x^2 - 9x + 15 - 5x^2 + 3x^3 = -9x + 15

Now, bring down the next term (-9x):

-3x^2 + 2x + 3
_______________________
5 - 3x | -3x^3 + 5x^2 - 9x + 15
-3x^3 + 3x^3 - 9x

Next, divide the first term of the new dividend (-9x) by the first term of the divisor (-3x):

-9x / -3x = 3

Multiply the divisor (5 - 3x) by the quotient (3):

3 * (5 - 3x) = 15 - 9x

Subtract this product from the new dividend:

-9x + 15 - (15 - 9x) = -9x + 15 - 15 + 9x = 0

Since the result is 0, there is no remainder.

Therefore, the quotient is x^2 + 3.

So, (15 + 5x^2 - 3x^3 - 9x) divided by (5 - 3x) is equal to x^2 + 3.