I have broken in four Remington R 5 Milspecs, three 308's, one 300WM. I like using Bore Tech CU+2 solvent which will take care of carbon and copper founding quite well. The Milspec barrels will break in fairly fast with 26 rounds.
-10 shots, clean after each round. A couple of wet patches, nylon brush one way/out 2-3 times, few wet patches, , couple dry patches. You should see the barrel start to clean easier after 4-6 shots.
-3shots/clean, 2X. Same cleaning procedure
-5 shots/clean, 2x . Same cleaning procedure.
-Done. I generally clean my barrels every 20-30 shots up to first 100 rounds. After that I'll usually clean every 50-100. I have fired as many 200 rounds before cleaning without loss of accuracy, or change in POI. Some may argue this but I think a proper break in supports this kind of performance, and makes routine cleaning a faster process.
I use the same cleaning procedure described above for regular cleaning and when finished I run a patch of Montana Blend Bore Conditioner.
I would not use an abrasive on the R5 barrel. It's not needed. Also, use the break in to zero your scope and test some loads.