To find the inverse of the function $f(x) = 5x + 3$ using algebra, follow these steps:

1. Replace $f(x)$ with $y$: $y = 5x + 3$

2. Interchange $x$ and $y$ (this step represents swapping the input and output of the function): $x = 5y + 3$

3. Solve for $y$: $x - 3 = 5y$ $y = \frac{x - 3}{5}$

4. The inverse function is: $f^{-1}(x) = \frac{x - 3}{5}$

Thus, the inverse of $f(x) = 5x + 3$ is $f^{-1}(x) = \frac{x - 3}{5}$.

Would you like more details or have any questions? Here are some related questions to explore:

1. How do you verify if a function is one-to-one?
2. How do you check if the inverse of a function is correct?
3. What are the properties of inverse functions?
4. How do you find the inverse of a quadratic function?
5. Can all functions have inverses?

Tip: To check if two functions are inverses, compose them: $f(f^{-1}(x)) = f^{-1}(f(x)) = x$.