The M1905 bayonet has a 16" blade. It was that long to make up for the shorter barrel of the M1903 rifle compared with the Krag. The Krag 30" barrel plus its 10" blade bayonet gave a "reach" of 40 inches.
After the original M1903 rod bayonet was found unsuitable, the rifle was changed to use a conventional bayonet, the Model 1905, with a 16" blade, duplicating the "reach" of the Krag with the 24" barrel of the new rifle.
Later, the Army later decided the M1905 bayonet was too unwieldy and adopted a new bayonet, the M1, with a 10 inch blade. The M1 designation had no connection to the M1 rifle; the bayonet was considered a weapon on its own and carried its own model designation.
The M1 bayonet was standard issue with both the M1 and M1903/A3 rifles. During WWII, a bayonet shortage caused Army ordnance to pull old M1905 bayonets out of storage and cut the blades down to 10", the same as the M1 bayonet. They designated those the M1905E1 bayonets. Some were cut and given a "spear point"; others were simply ground off at an angle.
Both the M1 and M1905E1 bayonets were in use through the Korean war; with the adoption of the M5A1 bayonet in 1953, both became substitute standard, though many remained in use with reserve units until the M1 rifle itself was phased out.
Incidentally, there are repros of the M1905 and M1 bayonets; the ones I have seen are poorly made and incorrectly marked, but the do deceive many new collectors. I have not seen any repros of the M5, but some were made by nations that received the M1 rifle under military assistance. The markings will distinguish those from US-made ones.
Jim