Depends on what kind of banjo you are talking about. A baritone uke is tuned DGBE. A plectrum Banjo is commonly tuned CGBD. Not that much different.
Of course Tenor Banjos sometimes use something called "Chicago tuning" Which is DGBE same as baritone uke.
5 string banjo is commonly tuned gDGBD or gCGBD. The little g being the short 5th (drone string) There are also several other 5 string tunings. You can't do these on a uke unless you add a 5th string. You could change out your 4th string (Low D), to a high D and tune dGBD which would be similar to 5 string banjo missing the 4th string. (The high d drone string would just be a different note in the open G tuning which will still sound good)
OR you could do what I did and go get a banjo. Good beginner models are Gold Tone CC-OT (what I have) or Deering Goodtime. Both excellent quality for the price.
If you are just looking for a different tuning, for a different style, you might consider slack key tuning– gCEG or GCEG. If you wanted re-enterant g, you would need a different 4th string.
I know this is an old thread, but I am posting a response so that anyone else who may do an internet search and find this can get a valid answer.
I am surprised no one else said this, but: The 5 string banjo is most commonly tuned gDGBD. All you have to do is tune your Bari Uku's 1st string down to a D from an E, and you have the DGBD of a 5-string banjo. Doesn't require any special strings or anything. All you are missing is the high g drone. I have been playing my Bari uke like a banjo (Both clawhammer and Scruggs), this for years. You can just use the 4th string (D) as a drone, or get creative and ignore the drone all together.
Take care.