The given terms of the geometric sequence are: -5, 10, -20.

In a geometric sequence, the ratio between consecutive terms is constant. Let the common ratio be $r$.

To find the common ratio: $r = \frac{\text{second term}}{\text{first term}} = \frac{10}{-5} = -2$ Now, let's verify this ratio with the third term: $r = \frac{\text{third term}}{\text{second term}} = \frac{-20}{10} = -2$ So, the common ratio $r = -2$ is consistent.

To find the next two terms, we continue multiplying by $r = -2$.

The fourth term: $\text{fourth term} = \text{third term} \times r = -20 \times (-2) = 40$

The fifth term: $\text{fifth term} = \text{fourth term} \times r = 40 \times (-2) = -80$

Thus, the next two terms are: $\boxed{40 \text{ and } -80}$

Would you like further explanation on this or have any questions?

Here are 5 related questions you might find useful:

1. What are the general properties of geometric sequences?
2. How do you determine the sum of a finite geometric sequence?
3. How can you find the general term of a geometric sequence?
4. What happens to a geometric sequence if the common ratio is a fraction?
5. How can you apply geometric sequences to real-world scenarios?

Tip: In any geometric sequence, if the common ratio $r$ is negative, the terms will alternate in sign.