I discussed the country genre with my wife some (she largely listens to modern country) and we came up with a possible lineup for five here:
Johnny Cash Probably something like The Legend of Johnny Cash - classic singer that appeals to a lot of people. His newer "American" series is great stuff, but less country. (a Merle Haggard greatest hits album is probably more classic country than Cash and is another option).
Reba McEntire - she has three different Greatest hits albums and a 2-disc "#1's" set. If you can count "#1 Hits" as one album, it's probably the best choice
Garth Brooks - The Hits - requirement since he led a revival in interest in country music
Kenny Rogers - I grew up hearing a lot of Kenny Rogers, so I consider it a must have, but it can be pretty cheesy. Despite many greatest hits albums, few have all of the songs I consider key. "20 Great Years" looks like a decent set.
Martina McBride - Greatest hits A great singer with some good stuff, probably deserving of the list.
As with all of these, there are probably better options or alternate lists.
BTW: With the jazz list and this list, many of these CDs can be had on the cheap via Amazon used section or yourmusic.com.