You just need to remove the spaces inside the character classes:
^5[1-5][0-9]{14}$
Those spaces are always meaningful inside a character class (even if you specify the RegexOptions.IgnorePatternWhitespace flag) and in your case they created ranges from space to space, not from 1 to 5 and 0 to 9 digits. Also, there is no need in the outer parentheses, you do not need to capture the whole pattern (you can always refer to the whole match with $0 backreference or match.Value).
See the regex demo.
As per @saj comment, you may now use
^(?:5[1-5][0-9]{2}|222[1-9]|22[3-9][0-9]|2[3-6][0-9]{2}|27[01][0-9]|2720)[0-9]{12}$
See the regex demo
Details:
^ - start of string
(?:5[1-5][0-9]{2}|222[1-9]|22[3-9][0-9]|2[3-6][0-9]{2}|27[01][0-9]|2720) - any of the alternatives:
5[1-5][0-9]{2} - 5, a 1 to 5 and any 2 digits (5100 to 5599)
222[1-9] - 2221 to 2229
22[3-9][0-9] - 2230 to 2299
2[3-6][0-9]{2} - 2, then 3 to 6 and any 2 digits (2300 till 2699)
27[01][0-9] - 2700 till 2719
2720 - 2720
[0-9]{12} - any 12 digits
$ - end of string.