"This started happening (or I only really noticed) sometime last year."

Did you make any changes to your banjo, or nut, or strings, or bridge position around that time?

Low hanging fruit first; not gonna talk about the truss rod, coordinator rods, head tension or tone ring binding.  This is a change of weather time of year, patience and time are often the best inaction as long as all the nuts and bolts are still firmly attached.

Check the string break at the nut and while you're at it; check the bridge too. 

Do this by wiggling the string side to side close to the live side of the nut.  

It should bend at or past the edge of the nut.  This indicates that the bearing edge is where it belongs.

If the strings are wiggling inside the nut; lift them, check for debris and rub pencil graphite in the slots.  Since the banjo(s) nuts and bridge worked fine in the past it's 'unlikely' that they were cut wrong.

Add the pencil graphite to the slots in the nuts and bridge even if things appear fine; it's a good thing.

It's a long shot, but check that the tuning peg is firmly connected.  Back the string tension off and gently check that the nut or screws holding the tuner to the peg-head are secure.  I just saw a banjo at the local jam with it's geared peg so loose that it had spun in it's hole.  This stuff happens, but, probably not to multiple banjos at the same time.

note:   Sometimes, my banjos go 'funny' without a good reason. I blame it on the weather, but it's a weak argument.  It just happened about two weeks ago and it's gone now.  Usually a little time, messing about and time fixes it...  Good luck.

Here's an abstract anwer/opinion.... (In short: try to live with it!) (long version below)

In the harmonica world most older harps were tuned with "Just Intonation". This allows you to play really sweet sounding chords while some individual notes sound ok but a little (or a lot) sharp/flat when played alone. There are also some harmonicas tuned with "Equal Temperament" that allow you to play perfect pitch notes individually but when a chord is played it sounds kind of awful. Most players do not use an equal temperament harp. Most harmonicas nowadays are tuned with a "Compromised tuning" which is somewhere in between the two options above, though leaning closer to the "just intonation" side. I would consider the banjo to be in the compromised tuning camp. You may have some sharp/flat notes when played individually but when you play clawhammer style/ oldtime/ whatever, in an open tuning it should sound nice. Hope this helps a little!

There are 247 things to check on a banjo!  Very few of them will have the symptoms that the poster describes.  Often, a little more information is needed to narrow down the possibilities. 
 

Only 1 string goes sharp, only in the first 5 frets, and started "sometime last year", which is not specified as 2024 or 2025.  Intonation on the 12th fret is accurate. 
 

Question to the poster:  if you put a capo on the first fret and tune the string accurately to
G sharp (Ab), are the next frets 2-6 sharp relative to the first fret?  
 

What we're trying to pin down is if the nut slot is the problem or not. 
 

The symptoms are consistent with the string not coming off the end of the nut but farther back. Need more information to decide if this needs further checking. 
 

Hope this helps. What else are you observing?

Thanks for the responses so far.

I'll go through the items suggested on Boxing Day and report back on the results.. I may even do my annual maintenance, string change, polishing, etc, while I'm in "tinker" mode.

Merry Christmas everyone!

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Originally posted by Adam Sea

Thanks for the responses so far.

I'll go through the items suggested on Boxing Day and report back on the results.. I may even do my annual maintenance, string change, polishing, etc, while I'm in "tinker" mode.

Merry Christmas everyone!

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If you haven't changed strings in a year I think we know what the problem is now. The first thing to get finicky when the core losses elasticity to my ears is usually the third string. It will start to to sound wonky and not in tune. Strings don't last a year if played. Try changing them one a quarter. When I was playing 5 or more shows  a week, I changed them weekly. I mostly teach and do far fewer gigs these days. I still change them every six to eight weeks to keep everything sounding good.

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Originally posted by Bob Buckingham

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Originally posted by Adam Sea

Merry Christmas everyone!

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If you haven't changed strings in a year I think we know what the problem is now. The first thing to get finicky when the core losses elasticity to my ears is usually the third string. (errrr.. the third string is usually solid and has no core)  It will start to to sound wonky and not in tune. Strings don't last a year if played. Try changing them one a quarter. When I was playing 5 or more shows  a week, I changed them weekly. I mostly teach and do far fewer gigs these days. I still change them every six to eight weeks to keep everything sounding good.

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I dunno about that Bob; it's true, strings do go wonky, occasionally. 

Most of the time they shift from an edgy cutting freshness to a steady predictable plateau at about the 6-8 week mark and stay that way for years of daily play. 

I like new strings, but, old strings have a predictably reliable tone that works well for many people.

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Originally posted by pinenut

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Originally posted by Bob Buckingham

quote:

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Originally posted by Adam Sea

Merry Christmas everyone!

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If you haven't changed strings in a year I think we know what the problem is now. The first thing to get finicky when the core losses elasticity to my ears is usually the third string. (errrr.. the third string is usually solid and has no core)  It will start to to sound wonky and not in tune. Strings don't last a year if played. Try changing them one a quarter. When I was playing 5 or more shows  a week, I changed them weekly. I mostly teach and do far fewer gigs these days. I still change them every six to eight weeks to keep everything sounding good.

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I dunno about that Bob; it's true, strings do go wonky, occasionally. 

Most of the time they shift from an edgy cutting freshness to a steady predictable plateau at about the 6-8 week mark and stay that way for years of daily play. 

I like new strings, but, old strings have a predictably reliable tone that works well for many people.

 

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As the old saying goes, mileage may vary. I can only speak from my experience. 

I bought a banjo years ago and ONE STRING would be extremely sharp. And I'm very used to the pecadilloes of Gibson fret spacing and all that! So I examined it really close with a strong magnifier and found the nut slot was cut wrong. The string was bearing way on the BACK edge of the nut. Gently used a nut file to knock that back edge down and get it to bear on the front. Problem solved.

Might be a nut slot(s) that's too high.