Jim W
The "H" head stamp is for the old Henry (Winchester) made ammo.
The "U" head stamp is for the Union Metalic Cartridge CO. which will become Remington (Remington/Peters) made ammo.
Without knowing the dia. of the bullet in the 5th cartridge you pictured compared to the other 4, it would be difficult to say which firearm this round was made for. Perhaps, Spencer's designed 56-52, but, it should be basically the same overall length as the other cartridges made for Spencer actions.
My best,
Blair