This device may be of interst to you:
**broken link removed**
It is adjustable, so you can set it to 12v. Bear in mind it is likely to dropout at 13v as it says it has 1v dropout, so may not provide good regulation down to 12.8 (unless you set the output to 11.8, if your circuit is ok with that). Alternatively, 5 more common 1A low dropout regs in parallel with small current sharing resistors could work. LM2940CT mabye.
A thought though, the voltage of said battery may well drop at 5A of load, due to internal resistance. I assume it is lead acid?, so it may be a negligable amount depending on it's capacity.