Best inexpensive source for cases with 5.25" and 3.5" bays is probably thrift stores. I've found that empty ATX cases and various cast-off systems from 2000s onward relatively common in thrift shops. Obviously this islocation dependent, but if you have thrift stores locally, I would start scouring them and see what turns up.
For modern cases, Fractal Designs cases are probably the best source for inexpensive + 5.25" drive bays. I bought a number of their Focus G cases over the past few years and a couple Define R5 cases. I use a Define R5 case in my all-in-one Pentium 4 build.
The Silverstone cases (FLP01 and FLP02) are the best for vintage looking with modern features. But they do carry a premium price tag. I am using an FLP01 case in a recent Pentium MMX build and really like it so far. While I wish it had more than just the one 5.25" bay, at least it can accommodate an optical drive.
When the FLP02 case comes available locally, I'll probably grab one of those as well. Just the fact it has 3 full 5.25" bays is amazing in a modern case.