Re: Sledding/sledging/tobogganing near Bern
The Gurten is great if you have your own sledge, and obviously very convenient!
Further afield, from Grindelwald there are 2 brilliant runs, where you're better off hiring their sledges. You will need to go with your 5 year-old, as you are literally sledging down mountain paths, occasionally crossing paths with skiers...
The Eiger Run - mountain railway up and sledge down...repeat as many times as you like. There is a nice bar/restaurant half way down!
Bussalp - Bus from Grindelwald to Bussalp, then there is a snow park (once there is enough snow), but also a long sledge run back down to Grindelwald.
If you go to the Gurten, let me know...we have an 11 and 6 year-old who would love to join your kids!