Mail drop between Waynesboro & Front Royal?

[A-Train]

You really won't need one. Its only 5 days. Almost all thru-hikers have no problem hiking 20 mile days. Shenendoahs are one of the most gentle sections of AT. There are waysides which have limited groceries as well as restraunts to supplement meals.
If you must, you can go to Luray, VA from Thornton Gap I believe, but rarely anyone does.

[Moon Monster]

The companion lists Elkton (US 33) and Luray (US 211), but as A-Train says, folks rarely go there. The hitch to Luray is 8 miles or so, but enough locals use 211 such that it wouldn't be the toughest hitch you have. http://www.aldha.org/companyn/va03.pdf
The Skyland or Big Meadows lodges in the Park might accept packages if you call first to announce/ask them.

[jollies]

There are lots of waysides and stores in the SNP right along the trail. I found myself stopping at them for meals and snacks a lot. Try looking into that. Although they are limited resupplies, you can probably find enough to get by for your breakfasts and dinners. Just carry 5 days worth of dinners.