Expected remaining time for bus to come, given that already waited for 5 minutes?

Question

There are two parts, one for when time is uniformly distributed and then an exponential distribution.

1. Time is uniformly distributed from 0 to 10. If already waited 5 minutes, what is the expected time remaining for bus to arrive?

2. Time is exponentially distributed with rate 0.3. If already waited 5 minutes, what is the expected time remaining for bus to arrive?

For first part, I was thinking that it would be 2.5 minutes because it would be a new uniform distribution given that you've already waited for 5 minutes. So the distribution would be (5,10) and it would be half of the time between that distribution.

For second part, I think that the waiting time would have no effect on the expected time left cause it's memoryless, so would it just be 0.3?