A cyclist records their cumulative distance cycled at the end of each day for 5 days. The cumulative distances are: Day 1: 134 miles, Day 2: 241 miles, Day 3: 336 miles, Day 4: 405 miles, Day 5: 500 m

The distance at the start is 0 miles. The distance at the end of Day 1 is 134 miles.

$$\text{Day 1 distance} = 134 \text{ miles} - 0 \text{ miles} = 134 \text{ miles}$$

The distance at the end of Day 1 is 134 miles. The distance at the end of Day 2 is 241 miles.

$$\text{Day 2 distance} = 241 \text{ miles} - 134 \text{ miles} = 107 \text{ miles}$$

The distance at the end of Day 2 is 241 miles. The distance at the end of Day 3 is 336 miles.

$$\text{Day 3 distance} = 336 \text{ miles} - 241 \text{ miles} = 95 \text{ miles}$$

The distance at the end of Day 3 is 336 miles. The distance at the end of Day 4 is 405 miles.

$$\text{Day 4 distance} = 405 \text{ miles} - 336 \text{ miles} = 69 \text{ miles}$$

The distance at the end of Day 4 is 405 miles. The distance at the end of Day 5 is 500 miles.

$$\text{Day 5 distance} = 500 \text{ miles} - 405 \text{ miles} = 95 \text{ miles}$$

Here are the distances cycled each day: 4) Day 1: $\boxed{\text{134 miles}}$ 5) Day 2: $\boxed{\text{107 miles}}$ 6) Day 3: $\boxed{\text{95 miles}}$ 7) Day 4: $\boxed{\text{69 miles}}$ 8) Day 5: $\boxed{\text{95 miles}}$