I wish mine looked so good. Your 5" barrel looks classier than the more common 4".

It is a K frame. S&W approves +P in steel K frames made recently enough to have been stamped with a model number or approximately 1958 and newer. However, that does not mean that a 1956 pre-Model 10 will bust on firing a +P cartridge. Lots of people have fired lots of +P .38 Special in revolvers like yours.