You guys nailed it...
On the dryer, it is indeed a 5.9 cu. ft. standard capacity. There was however a couple 6.9 cu. ft. models with the similar outward appearance of console and plug door. This model is timed dry only, no auto dry cycles.
As to the washer, I can tell you more. It is a 1974 model, 300 series. All Kenmores during this time period were relatively well featured for their series numbers, as even this 300 series has a pre-wash, two speeds, self-cleaning filter, and five temps.
This model, even in this color, was the first Kenmore that I completely re-built. I bought the machine from the outside backlot of a used appliance dealer for $5. I took it apart down to the last nut and bolt and even removed the baseplate from the cabinet. It did not need that but I just wanted to have done it. Having been sitting outside the face was a bit faded, but it was uniformly faded so I had no idea, and it still looked great. The cabinet was surface rusted though. I sanded it, coated it in anti-rust primer, and repainted it with Sears spray enamel in a can. It looked good but felt like sand paper...I wound up getting $150 for the washer a couple years later right in the knick of time before I moved to a new house. Later the returns pile from Sears coughed up another just like it.
It seems that I've seen more of these in colors than white, and I know of at least two or three Avocado machines and one white that I have stumbled across as well.
In 2012 I answered a picture-less Craigslist ad for a $30 Kenmore, and this is what greeted me:
