I live in Nashville and work in the television industry, so I have been able to see a lot of these guys in action. The 5-string really started to gain traction here during the early 90s. I think there are several reasons:
1. A very influential country producer(and record company chief) who was all over the charts in the 90s used 5-string players on many of his records. When that became "the sound", many other producers adopted the 5 in order to sound more like said producer.
2. More "lush" arrangements in country music have resulted in greater than ever numbers of keyboard and orchestral parts in the recordings. The 5-strings are just another tool allowing the country bassist to stake out his "space" in the record.
3. It is most commonplace for Nashville songwriters to "drop-tune" their guitars. D is the most commonly used tuning, but C is not uncommon. This results in lots of songs being written in these keys. While some artists will require transposition, many will sing it in the key as written, making it perfect territory for the 5-string. For many, many years, country was A and E-centric, but not so much anymore.
Whenever I go to a country awards show, the band risers are loaded with almost 100% 5-string basses. The lineup usually includes Sadowskys, StingRays, Fenders, and the occasional G&L. I would say that the 'Ray is probably the current "king of the hill" in this market.
If you looked back 30 years, the same scene would have probably been 75% split-coil P-bass/25% single-coil P-bass.