"One valid argument is that bulls eye target matches were fired in ten round stages, two five shot strings."
Except, it's not really a valid argument because the timing is off.
By the time Bullseye shooting became an established sport ammo manufacturers had been loading in boxes of 20 and 50 for several decades.
Formalized Bullseye matches grew out of the ISSF course of matches that were developed out of the shooting events chosen for the first modern Olympic games in 1896.
"And Colt Single Action Army revolvers were best carried loaded with five rounds."
Nor does that really work. The earliest self-contained metallic cartridge, the .22 Short, was being packaged in boxes of 50 or 100 (see my link above) before the Civil War.
And the Smith & Wesson Model 1 in .22 short...
Had a SEVEN round cylinder, so that math is especially jacked up.
Personally, I don't think there's any way to look at the number of rounds contained in a box of metallic cartridges and say "this number was chosen because of this gun or that shooting match."
From what I can tell, civilian manufacturers seem to have settled on the 20 round box for larger rifle cartridges and 50 round boxes for handgun and smaller rifle cartridges right around the time the Civil War ended.
The first post on this page shows a set of 6 early .32 Long rimfire boxes. The .32 Long was introduced by S&W in 1868 in their 1 1/2 revolver. The box in the upper right, from the US Cartridge Company (founded late 1868, began production in 1869), is extremely early, possibly pre-1870, and it's a box of 50.
http://www.cascity.com/forumhall/index.php?topic=48910.125
The math is also jacked up on this because the S&W 1 1/2 Model was a 5 shot revolver, meaning that it would be most safely carried with 4 rounds in the chamber.