5. Masha talked a lot on the phone with her friends, and the fully charged battery ran out exactly after 24 hours. It is known that the charge lasts for 5 hours of talking or 150 hours of standby. How long did Masha talk to her friends
Answer: $126 / 29$ hours.

Solution. In one hour of conversation, the battery discharges by $1 / 5$, and in one hour of standby, it discharges by $1 / 150$ of its capacity. Let $x$ be the number of hours needed for the battery to be fully discharged in 24 hours. Then, in standby mode, it will be $24-x$ hours, and the equation $x / 5 + (24-x) / 150 = 1$ is satisfied. Solving this equation for $x$, we get the answer.

An arithmetic method of solving is also possible. Every hour, the phone automatically discharges by $1 / 150$ of its capacity. Then, in one hour of conversation, it additionally discharges by $1 / 5 - 1 / 150 = 29 / 150$ of its capacity. Over 24 hours, the phone's battery automatically discharges by $24 / 150$ of its capacity, and the remaining part of the capacity $1 - 24 / 150 = 126 / 150 = 21 / 25$ was used for conversations. Therefore, Masha talked $\frac{21}{25} / \frac{29}{150} = \frac{126}{29}$ hours.

Comment. Correctly formulated the equation, but it was not solved, or the part of the battery capacity that it automatically discharged over 24 hours was correctly found - 5 points. For arithmetic errors with correct reasoning, deduct $1-3$ points.