ReflectedTime.cs

using System;

class Program
{
    static void Main()
    {
        int validTimeCount = 0;

        for (int hour = 0; hour < 24; hour++)
        {
            int newRightMinuteDigit = CheckAndReflect(hour, true);
            if (newRightMinuteDigit == -1)
                continue;

            int newLeftMinuteDigit = CheckAndReflect(hour, false);
            if (newLeftMinuteDigit == -1)
                continue;

            int newMinute = newLeftMinuteDigit * 10 + newRightMinuteDigit;
            if (newMinute >= 60)
                continue;

            for (int minute = 0; minute < 60; minute++)
            {
                int newRightHourDigit = CheckAndReflect(minute, true);
                if (newRightHourDigit == -1)
                    continue;

                int newLeftHourDigit = CheckAndReflect(minute, false);
                if (newLeftHourDigit == -1)
                    continue;

                int newHour = newLeftHourDigit * 10 + newRightHourDigit;
                if (newHour >= 24)
                    continue;

                validTimeCount++;
                Console.WriteLine($"Orig data: {hour:00}:{minute:00}, reflected time: {newHour:00}:{newMinute:00}");
            }
        }

        Console.WriteLine();
        Console.WriteLine($"Valid reflected time count: {validTimeCount}");
    }

    private static int CheckAndReflect(int number, bool left)
    {
        int digit = left ? number / 10 : number % 10;

        if (digit == 3 || digit == 4 || digit == 6 || digit == 7 || digit == 9)
            return -1;

        if (digit == 2)
            return 5;
        return digit == 5 ? 2 : digit;
    }
}