The standard tuning for 5 string banjos is gDGBD (the small g denotes the 5th string (more on that here)).
This is what I use 99% of the time. Pete Seeger is famous for popularizing the long neck banjo, which has three more frets and generally is tuned to eBEG#B. Alternate tuning patterns exist but I would recommend staying in the standard gDGBD until the standard tuning is very familiar. Moving to different tunings too soon can mess up familiarity with the banjo.
How to tune:
There are two methods to this. Tuning by ear and tuning by a electronic tuner. I would recommend tuning by electric tuner, at least while learning banjo. When I was learning banjo I tried tuning by ear too early and broke a string. Electric tuners run from $10 to $70 depending on the features. These would be fine for a beginner (Electric Tuner on Amazon.com). If you plan on playing with other instruments, it might be good to get a clip on tuner that attaches to the peghead. These generally tune by vibration, so it will pick up even in a noisy environment.
Tuning by ear is a little more difficult, and relies on hearing the differences between the correct tuning and the tuning on your banjo. Unless you have perfect pitch, you will need a reference you know is in tune. This can be a piano, another tuned instrument, or if desperate, a tone from some online source. I would avoid using a note from any online source, as the acoustics will probably be a little off, and tuning off of other instruments is a very useful ability.
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