Explanation:

To solve the expression $(34.85{)}^2-(18.99{)}^2-(5.01{)}^3$, follow these steps:

- Approximate the values involved:

- $(34.85{)}^2\approx (35{)}^2=1225$

- $(18.99{)}^2\approx (19{)}^2=361$

- $(5.01{)}^3\approx (5{)}^3=125$

- Substitute the approximated values in the expression:

$$1225-361-125$$

- Perform the arithmetic operations:

- First, calculate $1225-361=864$

- Then, subtract $125$ from $864$: $864-125=739$

- Compare with options:

- Option 1: 739

- Option 2: 673

- Option 3: 591

- Option 4: 807

- Option 5: 617

- Correct Answer: 739