The 5808 and 5208 may be drop-in exchangeable in eachother’s cabinets (not sure though - someone else may be able to clarify), however the fundamental layout of the 5820XL board is different from the 5808 or 5208, and so the 5820XL cabinet will not house a 5808 board out of the box.
If this is a hobby system and you’re willing to get creative, it might be possible to measure the mounting points and dimensions of the 5808 board and drill a couple new holes in the 5820XL cabinet to mount the 5808, however you probably won’t get all the standoffs secure without adding custom-fabricated separators and so it’s probably just better to wait until a decently-priced cabinet comes up on eBay. Once in awhile a 5808 or 5208 cabinet will surface for about $50 or so.