Reading the digits from behind is the same as reflecting them in a vertical line of symmetry. This means $0$ and $8$ are read as themselves, and $2$ and $5$ are swapped. Note that the digits are read in the opposite order
Since the time is before $10:00$, the first hour digit must be a $0$. When read from behind, this means the last digit must also be a $0$. Since the time is between $3:00$ and $10:00$ and the second hour digit must be one that reads backwards as another digit, it must be either $5$ or $8$.
Since $08:80$ is not a valid time, the time must be $05:20$.
This problem is taken from the UKMT Mathematical Challenges.