I guess Nintendo would be a recent demonstration in how coming out with new hardware in rapid succession doesn't necessary equate to a new generation of hardware. I used to think Switch would be considered a 9th gen system but... look at it, compared to the competition? It can't even run 8th gen games very well, if at all. Wouldn't surprise me if they put out another 8th gen level piece of hardware in the future "because Nintendo".
So you might consider 5200 as third gen the same as 7800, but 7800 is surely not in the same realm as SNES or Genesis, when it comes to hardware and capability. I don't think it could be considered as 4th gen.