A horse trainer has a bag of pink sugar mints for horse treats. She needs five treats per training session. The bag holds 24 mints. Which equation shows the number of horses that she can train and is a solution a viable option?

To determine how many horses the trainer can train with the given number of mints, we start by noting that each training session requires 5 treats and the bag contains 24 mints.

The equation that represents the situation is:

\[
5h \leq 24
\]

Where \( h \) is the number of horses. This inequality shows that the total number of treats needed for \( h \) horses (5 treats per horse) must not exceed 24 mints.

Solving the inequality for \( h \):

\[
h \leq \frac{24}{5} = 4.8
\]

Since \( h \) must be a whole number (you can’t train a fraction of a horse), the maximum viable option for \( h \) is 4 horses.

Now let's evaluate the options provided in the question:

1. **5h = 42, so h = 8.4 horses, which is viable.**
- This is incorrect because the equation \( 5h = 42 \) does not relate to our scenario and exceeds the available mints.

2. **h - 5 = 42 and h = 47, which is not viable.**
- This equation is irrelevant to the mints available as it suggests 47 horses, which is not achievable.

3. **5h = 42, so h = 8.4 horses, which is not viable.**
- This is the same incorrect relation as option 1, leading to more horses than mints available.

4. **h/5 = 42 and h = 210, which is not viable.**
- This equation is also incorrect because \( h/5 = 42 \) implies a need for 210 mints, far exceeding the available 24.

In conclusion, none of the provided options accurately represent a viable solution for the number of horses that can be trained with 24 mints. The correct conclusion is that the maximum number of horses that can be trained is 4, based on the available mints.