It seems to me that the question is not presented with sufficient care. 1 Corinthians 11:5 speaks not of the broad category of "women," but rather of "every wife." In addition the verses speak of a wife who "prays or prophecies;" not every woman who attends "public worship."
After researching this text my wife and I have decided that when she is placed in a situation (public or private) where it may appear that Christianity has "turned the world upside down" concerning traditional gender roles she should have "a symbol of authority on her head;"i.e. a prayer veil that covers her whole head. This is "because of the angels" (v. 10) not the culture. We also agree that this is in addition to her long hair which God has graciously provided as a covering for her as she worships and prays on an ongoing basis.