To simplify the expression 7x^2y^5 - 14x^3y^4 - 21y^3, we can factor out the common factors of x^2y^3:

7x^2y^5 - 14x^3y^4 - 21y^3 = y^3(7x^2y^2 - 14x^3y - 21)

Now, let's simplify the expression inside the parentheses:

7x^2y^2 - 14x^3y - 21

We can factor out the common factor of 7:

7(x^2y^2 - 2x^3y - 3)

Now, let's simplify the expression inside the parentheses:

x^2y^2 - 2x^3y - 3

There are no common factors in this expression, so we cannot simplify it any further.

Therefore, the simplified expression is:

y^3(7x^2y^2 - 14x^3y - 21)