Answer
See below.
Work Step by Step
According to the observer on the planet, the nap appears to last 35 minutes.
Find $\gamma$ at v = 0.99c. It is $\frac{1}{\sqrt{1-v^{2}/c^{2}}}$, or $\frac{1}{\sqrt{1-0.99^{2}}}$, which is 7.09.
The factor $\gamma$ is the time dilation factor. Multiplying 5 minutes by $\gamma$ gives 35.4 min.
According to the observer on the planet, the passenger’s watch is running slowly, and the nap lasted 35.4 minutes.
