Hello! Your answer would be 100 types of shoes.
To solve this, first take one aspect, add another, then add another.
First, look at the styles. There are five styles as of right now. Now, look at the sizes. For each one of the five styles, there are five sizes. This makes 5 * 5 types of shoes, or 25. Finally, look at the colors. There are 4 colors, for 25 types of shoes. 25 * 4 = 100 types of shoes.
Essentially, what this means is for these types of questions, all you have to do is multiply the number of choices for each aspect together.
Hope this helps!