I also have a brown 2005 P dime. I'm unable to weigh it. However, it appears to be thinner with a slightly smaller circumference when compared to other dimes. I don't think that it is brown because of an environmental result. I did an online search and came across another inquiry by the member GUN METAL. What are the odds that both of these dimes turned brown after minting? Has any professional information come forth regarding this dime?
Acid dipping can eliminate the clad layer and expose the copper core. Thus the thinner appearance. Gunmetal is a member that has not been seen on CoinTalk since Feb 2017.
Acquiring a scale as a collecting tool is imperative. I suggest one (around $10) which weighs to 2 decimals in grams and takes AA or AAA batteries (easy to change). Your dime most likely has environmental discoloration. It is quite common. Were it missing clad, weight would be less than normal. Dime weight missing one clad layer = 1.863 g +/- 0.091 g; missing two clad layers = 1.453 g +/- .161 g