Capo at Fret 1

One fret up, and the open-G system becomes an Ab system. Rarely used on its own, and the cleanest way to see the arithmetic with nothing else going on.

A neck capo at fret 1 raises the four neck strings by 1 semitone and leaves the short fifth string exactly where it was. That asymmetry is the whole subject: on a guitar a capo is one action, and on a five-string banjo it is two.

What it gives you

The open strings spell G with no capo, so at fret 1 the same system sounds in G#. Nothing about your left hand changes — the shapes are the shapes, and only their names move:

G → G#, C → C#, D → D#, Em → Fm, Am → A#m

The fifth string

The fifth string's nut sits at fret 5, not at the nut proper — the string is short and starts partway up the neck. So to raise it by the same 1 semitone, the spike or fifth-string capo goes at fret 6, which is 5 further along than the neck capo. The drone then sounds G# instead of G.

Capo at fret 1 — the neck strings, derived
StringOpenCapoed
4DD#
3GG#
2BC
1DD#

Doing it

Capo the neck first, then the fifth string, then retune — clamping a banjo neck almost always pulls something sharp, and a drone that is a few cents out is audible immediately because it never stops sounding. Check with the tuner before you play a note.

Your rolls are unaffected: a capo transposes the whole system and leaves the right hand identical, which is exactly the argument for capoing rather than retuning when all you want is a different key.