There are two different 4"x5" Graphic and Graflex backs.
One is the "standard" 4x5 two sheet film holder that does not have a groove on each side.
The other is the Graflex 4x5 two sheet film holder that has a groove on each side.
The second has a knife-like edges that slide into the two grooves while the first will fit into a Graflok holder or spring back.
It sound like the OP is talking about the "standard" holder for a spring back. However, too be sure, please post a photograph of your spring back on this thread.