I would use wood dust to match the fingerboard and wood glue. Make a paste and press into the wound. Wait a few days and lightly sand it out. Drill and install a new pip.
Or take to a decent luthier and have them repair it. They could fix the broken binding too.

What Gallaher said. There are luthiers who can repair this well enough you will never know it was there. And YES - the proper repair to begin with would have been to remove the broken fifth pip / nut and replace it with a new one..... Sometimes the best course of action when faced with what appears to be a minor fix.... is to consult with one who does this type work all the time. There are times when I wish I had taken the advice I just offered.... and NOW, I do.... (most of the time.... Ha ha!!)

I would cut away a portion of the fingerboard and fit and glue an ebony patch, not dust and glue, then re-drill for the pip.

I would take a piece of a binding- cut to the right size and glue it in with some two componett fixer

I would fill the split and holes as previously stated and redrill a new hole just behind the fret and install a brass post that sticks up higher than the fret and place the 5th strings on the inside of the post and directly onto the 5th fret.

On my banjo I filed half the post diameter and have the string nicely centered at the same spacing as the other strings.
Either reglue the old binding break or fit a new 1 inch piece rather than rebinding that whole side.

A cheap and easy fix would be to install a small, round (dome) headed slotted wood screw like the one that come on some cheapy Asian banjos. To install it, cut the old 'nut' off flush with the fretboard. Drill a small hole and screw the screw in. Make sure the slot is slightly higher that the fretwire so the string can sit above the wire. By turning the screw, you can lower or raise the string. Just my 2c worth.

"... and that's how I started playing plectrum banjo." 

My main banjo just has the 5th strings on top of the fret (on the outside edge of the no-longer used pip) and stays there all on its own.
These frets end at the outside edge of the binding giving a wide support under the string.

quote:

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Originally posted by steve davis

My main banjo just has the 5th strings on top of the fret (on the outside edge of the no-longer used pip) and stays there all on its own.
These frets end at the outside edge of the binding giving a wide support under the string.

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There has always been two schools of thought as to where the 5th string sits. Does it sit behind the fretwire in a nut/pip, or sits ON the fretwire, held in place by a nut whose slot is cut deep enough for the string to bend over the fretwire, or by a 'spike' just behind the fretwire (Deering?).

My personal preference is the nut behind the fretwire and the string sitting above the fretwire. Just my 2c worth.

On my main banjo (not pictured here) I simply took the string out of the pip slot and set it directly on the end of the 5th fret.
It goes directly to the tuner from the fret.
I could remove the pip entirely with no effect on the string.but I leave the pip in place because it looks better that way.
Jimmy Cox has the pip positioned halfway through the 5th fret which also intonates very well when thumbfretting or spiking.