Take a look at our recommended games page for some ideas. It's not an exhaustive list by any means, but they are games that we have personally evaluated and were rated favorably.
Based on your description, I would say that Gold Mine, Ticket to Ride, and Eruption would be good choices as they all accommodate 5 to 6 players (I designed Gold Mine and Eruption, so take that with a grain of salt - but I truly think they are good for your situation). If you think they would like cooperative games, Castle Panic is a great choice, as well.
Take a look at our recommended games page for some ideas. It's not an exhaustive list by any means, but they are games that we have personally evaluated and were rated favorably.
Based on your description, I would say that Gold Mine, Ticket to Ride, and Eruption would be good choices as they all accommodate 5 to 6 players (I designed Gold Mine and Eruption, so take that with a grain of salt - but I truly think they are good for your situation). If you think they would like cooperative games, Castle Panic is a great choice, as well.