You can say "a five-minute walk" or "five minutes' walk". Note the use of the hyphen in the first and the apostrophe in the second. As usual with complex nouns, there's also the third alternative - the 'of' construction. We use this if we want to put in some kind of modifier e.g. "It's a walk of only about five minutes."
You could add an 'a' to "five minutes' walk", but I can't see any grammatical justification for it. Here's why:
You need an article in the first, because 'five-minute' is an adjective - just as you'd say 'a brown-eyed girl', you need to say 'a five-minute walk'.
We don't need an article before the genitive form, though. Think of "Mum's car", "China's economy" or "Wednesday's meeting". The use of the genitive case makes this a definite noun, so it strikes me as wrong to use an indefinite article. In the overall scheme of crimes against humanity, there are worse things to worry about, but..