2nd the recommendation for a chamber cast. There are several 6.5mm pre-war cartridges. If the rifle is a Mannlicher, it is probably the 6.5 x 54 Mannlicher Schoenauer, sometimes called the 6.5 x 53, depending on who made the ammo. Both have a relatively small case body diameter, considerably smaller than the 7 x 57. But there was also a 6.5x54 Mauser. The 6.5 x 55 case is fatter than 7 x 57 family of cases and might not chamber. There are also at least 2 different 6.5 x 58 cartridges and a 6.5 x 61 that is very close to a .256 Newton. And probably others.
