5. Solution. Let the probabilities of heads and tails be $p$ and $q=1-p$ respectively. We form the equation

$$
C_{10}^{5} p^{5} q^{5}=C_{10}^{6} p^{6} q^{4}
$$

from which we find: $252 q=210 p ; \frac{p}{q}=\frac{6}{5} ; p=\frac{6}{11}$.
Answer: $\frac{6}{11}$.

## Grading Criteria

| Solution is correct and well-reasoned | 2 points |
| :--- | :---: |
| Correct equation is set up, but an error is made or the solution is not completed | 1 point |
| Solution is incorrect or missing (including only providing the answer) | 0 points |