Context is important. St. Paul is speaking of a woman who is "praying or prophesying."

 5 But every woman praying or prophesying with her head not covered, disgraceth her head: for it is all one as if she were shaven.
 
6 For if a woman be not covered, let her be shorn. But if it be a shame to a woman to be shorn or made bald, let her cover her head.

It's really telling how some 'Catholics' dislike being told by Catholic Saints that women should cover their heads in public.

 Notice how St John makes it very clear that women should ALWAYS be covered. Gray when you say that women should only be covered during prayer you are interpreting scripture according to you own will. But being Catholic we ought to agree with those Saints who are far greater than on understanding scripture.

As it is written.

30 And Philip running thither, heard him reading the prophet Isaias. And he said: Thinkest thou that thou understandest what thou readest?

 31- Who said: And how can I, unless some man shew me? And he desired Philip that he would come up and sit with him [Acts Of Apostles 8:31]

The man indeed ought not to cover his head, because he is the image and glory of God; but the woman is the glory of the man.
[1 Corinthians 11:7]

St Augustine takes this further saying that a women is only the image and likeness of God when she is with her husband. Men will understand this, feminists will gnash with the teeth.

I often say that men should wear hats and ties and well polished shoes. A tie has the added advantage of being an item of clothing that only men wear, and is therefore a strong marker of virility. Just a woman in a dress is strong public marker of femininity.

Anthony, why do you continue to take Holy Scripture out of context?
Context is important. St. Paul is clearly speaking specifically  of a woman who is "praying or prophesying."

 5 But every woman praying or prophesying with her head not covered, disgraceth her head: for it is all one as if she were shaven.
 
6 For if a woman be not covered, let her be shorn. But if it be a shame to a woman to be shorn or made bald, let her cover her head.

Women should wear the veil when in public. Jeans and pants should also be outlawed for women. Anything tight and revealing should also be banned.

When it comes to men, shorts that are above the knee, and tight fitting clothes. Men wearing tight fitting clothes is just effeminacy. For the sake hygiene, beards and hair should be trimmed as well.