Derek divided **5/8 of a gallon** of ketchup equally into **5 smaller bottles**. To find out how much ketchup he put in each bottle, we need to divide the total amount of ketchup by the number of bottles.
To calculate this, we can use the following formula:
```
Amount of ketchup in each bottle = Total amount of ketchup ÷ Number of bottles
```
Substituting the given values into the formula, we get:
```
Amount of ketchup in each bottle = 5/8 gallon ÷ 5 = (5/8) ÷ 5 = 5/8 × 1/5 = 1/8 gallon
```
Therefore, Derek put **1/8 gallon** of ketchup in each bottle.