Does "away" serve as an adverb or an adjective in the following sentence?

Solution 1:

Sometimes away can be an adjective.

The OED has an adjectival sense for away in its sense 11a:

11 a. Of the position attained by removal in place: In another place; at a distance; at (a stated) distance, off. spec. In reference to games or matches played away from the home ground. Hence as adj.; also as quasi-sb., a win away from home.

On of whose provided citations is quite similar to your own example:

• 1881 Blackmore Christowell xxxix, — His home was some miles away.

Then again, you can find people these days who will try to convince you that something like ago is not an adverb but a postposition. If you’re on their side, then I see no difference between “five minutes ago” and “five minutes away”. I’m pretty sure that whatever they are, ago and away are doing the same job in those two phrases.

Solution 2:

"Five minutes [' journey] away" is a deictic locative predicate, as John Lawler argues. I'm not sure how proximal – possibly distal.

The implication (see his answer) is that insisting on using 'adjective' or 'adverb' (or 'preposition. . .') labels out of the bag-of-eight for all words in this type of construction is doomed.

'. . . is here / five miles away / five minutes away'

seems to rule out adverbial classification for such constructions, while

' . . . lies/stands here / five miles away / five minutes away'

seems to require it.

However, the deictic tie-in is not typical of either adverbials or adjectivals.