This here eBay ad got me thinking:
https://www.ebay.com/itm/Antique-Vtg...53.m1438.l2649
That is quite clearly a Mexican vihuela, not a mandolin; it even says so on the label. The vihuela has 5 strings and provides harmony to the lead guitar in mariachi music. It is typically tuned ADGBE, but in a re-entrant tuning so the A, D, and G strings are an octave higher than they would be on a guitar.
It looks OK for the money, although it would be nice to have a few more frets. I wonder about tuning one FCGDA and playing it as a 5-string tenor. But maybe that's a silly idea.
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