I have a Martini action  sporter bought as .380". Now looking at getting it running I am not so sure. I believe the cases were the same but the bullet diam only differs.The bore comes out as best I can measure  as it  is 5 grooves at .365 ". Is this a .360 not .380? and any advice especially on bullets would be gratfully received. Entry on FAC means I should get this clear. Thanks in advance.

Bill is correct in that the bullet dia for .36 no 5 is .365: but I have measured two .380s over the years and they were the same!
When you buy a rook rifle. insert a case into the breach and close it. Drop a slightly undersized length of lead wire down the barrel and slowly and gently tap it down woth an old rod. Open the breach, extract the case, with the help of the rod, and measure the lead plug. Most of them are a long way from the nominal calibre.
Fred.

Actually, .38 special hollow based wadcutters give the best results in either of the nominal calibres. You may need to trim the brass back a few thou.
Fred.