One of the best barrel IMO for the A5 is the J&J ceramic. It does everything the above mentioned Ultrlite does but for around $40. It is coated with ceramic so with any breaks it'll shoot itself clean after 2 shots, is just as quiet as a Stiffi barrel and very accurate. I have a 12" J&J now as my main barrel, I made the switch from a 12" Stiffi carbon fiber barrel that had practically the exact same performance but cost me $109. All that being said the best thing you can do for accuracy is a barrel kit followed by air consistancy. J&J also make the Edge barrel kit ranging from $95 to $150 for the three kits.
Here's the link to their site.