Munich airport

If anyone in your party is interested in historic airliners, there is a good display in the Visitors Park adjacent to the airport terminal.

If that is 5H20M between flights, you'll have to be back some amount of time (1 hr) before the next flight leaves and it will take you some time to get off the plane and find the S-Bahn station, so you would probably be down to 4 hrs or less actual time. It takes about 40 min from the airport S-Bahn station to Marienplatz or back so your down to a dwell time at Marienplatz of about 2+ hours. You'd have to decide if 2 hours at Marienplatz is worth the hassle and risk of missing your flight out.

If you do decide to go into Munich, at Marienplatz is the New Rathaus, a shopping mall, and the Frauenkirche (church with green cupolas). Take the S8 from the airport to Marienplatz. Even if the S1 leaves first, it takes longer and will only get you to Marienplatz one minute sooner. On the way back, also take the S8. At worst, you'll get back to the airport 9 minutes later, but you will avoid the chance of being on the wrong end of the train when it breaks at Neufahrn and ending up in Freising.

The S-Bahn station in Marienplatz is on two levels. Make sure you get the right level (the upper one) for the S-8 to the airport. The S-8 on the other level (the next one down, the one you came in on) will take you west of town, nowhere near the airport. The level you want says Richtung (direction) Ostbahnhof; the wrong level says Richtung Pasing.

A better option, depending on the time of day, might be to take the 20 minute bus ride ( No. 635) to Freising and another bus (638 or 639, 6-8 min + 10 min walk) to the Weihenstephan brewery (the oldest in the world).

There is a micro-brewery and a beer-garden right outside Terminal 2 on a very lively square. Quite nice there!

Also you could take a cab and have them take you into the city center of Erding (where the Weissbeer is from) - a lovely, picturesque Bavarian small-town - and about 30 minutes from the airport.