Dan -
That washer needs a good loving home. I have had it at least 11 years, and it went straight into storage without even being tested. One of my customers referred a friend of hers to me, who was moving and wanted to get rid of two older Kenmores, this washer and an avocado match-all dryer from the early 70s. I got them and gave the dryer to my good buddy, who was experiencing a dryer shortage at the time and needed it to make a set for sale.
Anyway, the 500 series is just part of the line-up that goes from 100 to 900. Some machines make more "advertisement" of their series than others, and the same was/is true in certain eras. The most common series are the 60/600, 70/700, and the 80/800.
Right now, new Kenmores seem to have 500, 600, 700, etc. on them (top loaders). In the 1980s it was 60, 70, 80, 90. My mom's 1974 Kenmore 60 series didn't say it's series anywhere. I am not sure I ever saw 500 or lower written on a machine (maybe a 400?). But, the line starts with the 100 series, which is usually a single cycle, single knob deal with no water level selection and timer set temps. BOL for sure. As the line went up, features were added. Oddly, in the 60s, the 400 was the BOL, but when Sears added features and less change per model, they needed more series numbers.
The 100, or 600, etc. are parts of the actual model number, so one can tell what series the machine is whether or not the console says so.
This machine has a 500 series counterpart that doesn't have the pre-wash or pre-soak, and does have the manual filter. I need to take a picture of it. It's a better example of a 500 series. This one is odd to have those cycles and the self-cleaning filter. It does have a straight vane agitator, since Roto-Swirls didn't usually appear until at the least the 60-series.