To solve the equation, we can start by simplifying the expression on the left side:

5x(x-3)^2 - 5(x-1)^3 + 15(x+2)(x-2) = 5

Expanding the squares and cubes:

5x(x^2 - 6x + 9) - 5(x^3 - 3x^2 + 3x - 1) + 15(x^2 - 4) = 5

Distributing the terms:

5x^3 - 30x^2 + 45x - 5x^3 + 15x^2 - 15x + 5x^2 - 20 + 15x^2 - 60 = 5

Combining like terms:

5x^3 - 5x^3 - 30x^2 + 15x^2 + 15x^2 + 5x^2 + 45x - 15x - 15x + 15x^2 - 60 - 5 = 5

Simplifying:

45x - 60 = 5

Adding 60 to both sides:

45x = 65

Dividing both sides by 45:

x = 65/45

Simplifying the fraction:

x = 13/9

Therefore, the solution to the equation is x = 13/9.