My partner and I will arrive at Barajas from Malaga, on our way back to the US at 1 PM, but our flight to Washington doesn't leave until 5:30 PM.

Any thoughts about how we might spend those hours, other than staring at bad TV in a molded plastic chair? Any mini-excursions come to mind or at least an interesting place at/near the airport for lunch?

Restaurant Pato Mudo at Hotel Diana is a nice place for lunch; but it is a favorite among local businessmen so it may be crowded. If you dine on the Terraza try to make sure you are not in 'pleno sol.' It can get pretty hot.
Or, you might consider going up to the departures roadway and catching the 101 bus to the plaza in Barajas pueblo. Toribio's Churreria will be closed at 13:00 but you should have no trouble finding a pastry shop or cafeteria.
I am assuming that your bags are checked thru and you already have your seat assignments. If not, just stay at the airport.

Just a last precaution, Barajas is not a big airport, but it can be tricky for transfers if you are short on time.

Since you will probably be arriving at Terminal 2 and leaving from T1, make sure you know the way to get into T1 when you go back.

Worst case for transfering is arriving at T3 or the "nort peer", and departing from the extended peer or T1, that is a good walk and path is not always evident.

This should be a popular thread - Barajas just achieved the "honour" (again?) of being Europe's worst international airport in terms of number of delayed flight departures!

on a related topic....
I have a 7 a.m. out of Barajas. If I showed up around midnight the night before can I find a comfortable floor to sleep on in relative security???

You are lucky, if you don't mind waking up early, first flights are normally the best flights on time,.....