You did not tell which regex implementation you use.
^[a-z0-9](\.?[a-z0-9]){5,}@g(oogle)?mail\.com$
[a-z0-9]
first character(\.?[a-z0-9]){5,}
at least five following alphanumeric characters, maybe preceded by a dot (see @Daniel’s comment, copied from @Christopher’s answer)g(oogle)?mail
gmail or googlemail (see @alroc’s answer)
Probably you will want to use case-insensitive pattern matching, too. (/.../i
in JavaScript.)