Example 4. A discrete random variable $X$ has the following distribution:

| $X$ | 3 | 4 | 5 | 6 | 7 |
| :--- | :--- | :--- | :--- | :--- | :--- |
| $P$ | $p_{1}$ | 0.15 | $p_{3}$ | 0.25 | 0.35 |

Find the probabilities $p_{1}=P(X=3)$ and $p_{3}=P(X=5)$, given that $p_{3}$ is 4 times $p_{1}$.