Can an E3 on title 10 NG orders marry an active duty E5?

PFC (Join to see) I do not see an issue with it. As long as you maintain a professional relationship when on duty, and personal problems don't cause military problems, you should be good to go.

EDIT: You should also review the appropriate regulations for more information, and understanding.

Actually this is a very interesting question. It is a little known fact that you cannot be punished for 'marrying' anyone. Fraternization and unprofessional relations rules apply to relationships, not marriage, and once you are married, that marriage overrides EVERYTHING. Now with that said, Chain of Command will NEVER allow married people to be in the same chain of command, so it might very well be bad for one or the other spouse's career plans, but marriage to anyone is not punishable.