So where did the 5/1-3-1 come from? Is it legitimate or a novelty?

It comes from whatever the number of shakes the altar boy decides at the time he rings the bells. Always has, always will. Is that legitimate or novelty I don't know, all I know is in this matter, it is always up to the whims of the altar boy who is ringing the bell.

I served and went to many Masses that used a simple dinner bell, good luck ringing that bell only 3 dings. The important thing is *when* it rings, not how many rings it makes.

…Always has, always will. …

Except when it hasn't and won't.

The rubrics for a low/high mass are 3 rings.  The 1-3-1 is sometimes used at a solemn high mass, for added solemnity.  Otherwise, it's probably an typical-french-sspx-influence where they use the 1-3-1 for low masses.  The french influence in the sspx cannot be overstated and it shows itself both in liturgy and in theology.  Sometimes good, sometimes bad.

While Mark 79 shows hand missals that reference one "bell", I've often seen (in fact, I've only seen) altar boys with altar bells--three bells connected together!  

Obviously, then, there are 15 bells being rung instead of five!  Oh! The humanity!  

Notice these missals mention the bells ringing 3x.  Not 1-3-1.  Not 5x.  Only 3x. 
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I've often seen (in fact, I've only seen) altar boys with altar bells--three bells connected together! 

Exactly.  And this corresponds with the 3 actions of the priest - genuflection - elevation - genuflection.  It's not that complicated.
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The liturgical differences can only be attributed to european customs...

@Matthew

Is this a trad forum or not?

If it is a trad forum, is it legitimate to discuss rubrics of the trad Mass, including the bells?

Further, both the Stedman's and the St. Andrew Missals (as posted above) blow your "never" to hell.

Even though you were wrong, this tempest-in-a-teapot is hardly worth your typical over-reaction.

1. Who is over-reacting? Who just posted like 10 times in a row, having clearly spent hours on it, scanning and posting pages from various missals? Give me a break.
2. Yes, this is a trad forum. Any other childish questions you need answers to?
3. Who said this thread should be deleted or purged? Certainly not me. The thread still exists doesn't it? I obviously have no problem with it.
4. I still hold that this is a tempest in a teapot. You haven't proven me wrong here. Or have you demonstrated that this is critical to the Faith of Catholics, and I missed it? Trads have much more serious things to worry about than the CUSTOM of how many bells to ring at Mass. Those missals just express the local custom, they aren't rubrics or dogma. Only the Missale Romanum is official. Hand-missals for laymen just put into printed form the rubrics *as well as the most common local customs*.

The only rubrics that matter are the ones in the ACTUAL priest's missal.  The layman's missal isn't designed to be explanatory in this aspect.