The 5.0 L engine is generally used to refer to the Ford 302. Oldsmobile offered a 5.1 L engine that was actually a 307. You can find a 307 in practically any 80s or early 90s Cutlass (as long as it has a V8), Delta 88, 98, or Custom Cruiser. However, most people here will tell you that for a mild performance build you will be much happier with a 350 or 403. Externally, there is no difference between the 307, 350, and 403 (besides color).
I suggest you find an Olds 350. These can be found in 70s Oldsmobiles like the Cutlass and Delta 88. The good thing about Oldsmobile engines is that your car will be a perfect fit for an Olds 350. The biggest obstacle will be upgrading your transmission. Currently, your car probably has a 200 4R, 4 speed automatic. These are good transmissions; however, it might have to be beefed up to withstand the output of a mildly built 350.
1971 Oldsmobile 98, 455 (of course)
2011 Ford Flex, 3.5L Duratec V6
2003 Ford F150, 5.4L Triton V8