Lets look at the nomenclature. This is more for me to understand the question. Someone please clarify if I made any mistakes. Savage changes models from year to year so if it is not shown it does not mean that it was never made or does not exist. I would post a link for you to type in your serial number to get the correct nomenclature of your rifle from savages website but you would have to wait until the 15th to be able to do the search. Currently the site is down for maintenance.
Model 10 FCP HS Precision 308
Model Number- They don't make a 10/110. This is the way it is listed on the web site to cover more than one action length. It is probably a model 10 for Short Action. Model 110 is for long action. 308's in you model were a short action. So model 10
http://www.savagearms.com/firearms/models/
F- Synthtic
C- DBM
P- Police
H-S Precision- Stock manufacture(aftermarket).
Your rifle is listed as and to the best of my knowledge a right hand twist of 10:1
Regardless of what twist and type of rifling your rifle has it does not say 5R. So to better understand your question, what help you make the the jump from standard rifling to 5R?
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