Have you looked into the MIJE hostel or any of the ones affiliated with Hostelling International? With 5 of you, you can pretty much have your own dorm room in a 6-share if you book ahead. Look at reviews on Hostelworld.com or BUG.
How about looking into university housing if you are going during the summer months? Many colleges and universities in Europe are now renting beds to tourists in their dormitories.
You may also want to check into renting an apartment (though you'll have to come up with money for a deposit) for a few nights.
Finally, if you want to get adjoining rooms at a budget hotel, try the Ibis or Accor chain. They sometimes offer good rates and have locations all over the city.