Chris,
This grill fits none of the definitions I see posted over the years.
I contacted Weber and they stated it was an 1988/1989 Genesis 5 LP based on the serial #L5.
Sure doesn't look like a 28 year old grill.
It doesn't have the side burner like the 5000 models do.
I Found this helpful past post from Weber employee Joe Osborn :
"It's a Genesis 5000. You could confirm this by looking at the serial number. If it starts with a "KL5" or "KN5" it is a Gen 5000 from 1993 (the first year they had glass doors) or a S/N starting with EH, EO, ER, EI, EZ, or EE. If it is a two letter code, I would need the complete S/N to confirm the model. Production for this grill started in 1993 and ended in 1999 though some of the later models had stainless steel doors according to the info we have. I hope this info helps."
Jeff