If you don't know REGEX, you may not use it for such simple tasks.
Try instead this clearer approach:
private static bool TestString(string s)
{
if (s.Length < 2) return false;
switch (s.Remove(2))
{
case "00":
case "07":
case "16":
case "23": return true;
default: return false;
}
}
Not everything should be done with regexes!