I am a new ham and I was just given a G5RV Jr. I have about 20 feet of coax plus about 60 feet of 450 ohm ladder line I can feed it with. Can I extend the G5RV Jr. feed line with the ladder line I have, and then connect it to the coax and still tune it successfully? Would I need the recommended 1:1 balun, or something else? Thanks.
That length of 450 ohm ladder line is important. In order to have a reasonable VSWR on the bands that the G5RV was designed for, you should not change it unless you want to cover different bands.
The G5RV and the "Jr.", while good antennas on some bands, was invented before antenna modeling programs (such as EZNEC) were available. After they were, ZS6BKW modeled it and changed a few things.
I have my own improved variation of this antenna design. Much more information about this is here.
A G5RV antenna extended with more ladder line is just a dipole with a ladder-line feed.
You certainly can do that, though to call it a G5RV isn't really accurate. Like Mike Waters explains, the length of the ladder line in the G5RV design is important, as it's part of a stub match.
Even though the result is no longer a G5RV, you may still get a decent antenna since even cheap ladder line has loss comparable to good coax, and thus even a moderately high SWR on the feedline may result in acceptable losses, especially if you either get lucky or fiddle with the dipole length such that the SWR isn't astronomical on any band you intend to use.