a regular expression that is a half-width number up to five digits and does not allow "0 only"

Why don't you use the negative read-ahead assertion (?!...) to exclude "only 0" first?I think negative look-ahead can be used in most processing systems.

^(?!0+$)\d{1,5}$

On Python, I tested the following and found everything.

import re

pattern=r'^(?!0+$)\d{1,5}$'
print(re.search(pattern, '0'))

For Java, the regular expression is the same.The look-ahead should be used in the same way in recent programming languages.

String str="0";
String pattern="^(?!0+$)\\d{1,5}$";
Pattern p = Pattern.compile(pattern);
Matcher m=p.matcher(str);
System.out.println(m.find());