I think it really depends on the location. If it's in the village I'm living right now I don't think 2000 CHF is enough for 5 rooms.
The standard for 3 rooms is CHF 1600-1900/month.
The online sites are good to know about the price range but not really effective in renting them.
I would also suggest to try contacting the local agent rather than the big online ones, because what happen in my case was the apartments that were advertised there are no longer available.
What I did then I contacted several local agents by e-mail describing the criteria that I needed and then they'll give me a list of what they got then I can set up a time to visit the apartment before deciding on renting anything. Because sometimes, according to my experience the condition is 'slightly' different then what is advertised