Explanation:

- Consider $(9.979{)}^3$. Approximating, it's close to ${10}^3$, which equals 1000.

- Next, $(23.99{)}^2$ is approximately $(24{)}^2$, which equals 576.

- Finally, $(1.99{)}^5$ is close to $2^5$, which equals 32.

Now, calculate the approximate expression:

- $1000-576+32$.

Breaking it down further:

- $1000-576=424$.

- $424+32=456$.

So, the expression approximately equals 456.

- Option 1: 350

- Option 2: 490

- Option 3: 390

- Option 4: 420

- Option 5: 450

The option that’s closest to our approximated value of 456 is Option: 5 - 450.