pre hung doors to fit into old frame
All you need to do is install the door with what is called a "jamb extension". Just get some strips of 5/8"x3/4" inch molding, then glue them to the non-hinge side of the new door jamb.  On a painted jamb these will for all intents and purposes disappear with sanding and some wood putty.  On a stained jamb you'll be able to see the extension, but you can minimize how much it stands out by picking wood with a similar grain pattern.