To solve $5^{-1} + 4^{-1}$:

1. Calculate $5^{-1}$: $5^{-1} = \frac{1}{5}$

2. Calculate $4^{-1}$: $4^{-1} = \frac{1}{4}$

3. Now add the two fractions: $\frac{1}{5} + \frac{1}{4}$

To add these fractions, find a common denominator, which is 20:

$\frac{1}{5} = \frac{4}{20} \quad \text{and} \quad \frac{1}{4} = \frac{5}{20}$

Now, add them:

$\frac{4}{20} + \frac{5}{20} = \frac{9}{20}$

Thus, the final result is:

$5^{-1} + 4^{-1} = \frac{9}{20}$

If you have any questions or need further details, feel free to ask! Here are some related questions:

1. How do you calculate powers of negative exponents?
2. Can you explain how to find a common denominator?
3. What are some properties of exponents?
4. How can this concept be applied in solving equations?
5. What is the significance of fractions in mathematical operations?

Tip: Remember that a negative exponent indicates the reciprocal of the base raised to the positive exponent.