It's generally believed that if you want play bluegrass music you HAVE TO play it on a five-strings banjo. In fact, with an adjustment in tuning, the 17-fret tenor banjo does the job very well. The standard tenor tuning is CGDA. The high string A can be lowered one step to a G note which can serve as the drone for an open G tuning. This G note is equivalent to the short 5th string on a 5-string banjo. Since it is an octave above the middle G it is labeled as "g". The low C string could be left as it is and the instrument played in a C tuning. But for bluegrass effects which generally occur in G tuning, the low C string is raised one step to a D note. Now we have the sequence of DGdg. Since the second string is an octave above the low D it is labeled as "d". Of course this tuning can be used to play irish music, clawhammer, or jazz. With only a slight modification in the fingering, all the standard tenor chords can be fully used.
 
There are some advantages of the tenor banjo.The necks (being shorter) don't tend to warp as much, they cost considerably less than their 5-string counterparts, and there's a much better selection of them among the vintage instruments. Here are some tunes fingerpicked on a tenor banjo tuned to DGdg