Banjo B♭sus4 chord (Double C)B♭ suspended 4th on the 5-string banjo: 3 3 3 3, and 3 more shapes

Frets, string 4 to string 1: 3 3 3 3 (first position)

1. String 4 (C): 3rd fret, index finger (barre), E♭
2. String 3 (G): 3rd fret, index finger (barre), B♭
3. String 2 (C): 3rd fret, index finger (barre), E♭
4. String 1 (D): 3rd fret, index finger (barre), F
5. String 5, the short g: open, G, not in the chord

Sounds: E♭ B♭ E♭ F  ·  B♭sus4 is B♭, E♭, F (1 · 4 · 5)

The 5th string: the short g adds the 6th over B♭sus4, a colour rather than a clash.

With a capo: on the 3rd fret it’s 0 0 0 0 (frets counted from the capo), an open Gsus4 shape. Spike the 5th string at the 8th fret to keep it in tune with the capo.

Double C tuning: gCGCD, the short 5th string first, then strings 4 to 1.