TubeNet

1. How much current does the gadget use? If it uses no more than 4.5/5 of the rated current the adaptor can deliver, no problem. Most of these odd-voltage setups work because a nominal 1.5 volt alkaline battery actually delivers 1.6 to 1.7 volts when new, so that's actually 4.8 to 5.1 volts.

2. OTOH, most modern gadgets have some sort of circuit protection built in, so running the 6 volt side should not be a problem.

3. Finally, inexpensive adaptors are notorious for inconsistency. I would take a multimeter and check to see what the actual voltage at the tip really is, knowing that under load it will be slightly less. Then I'd use the setting that is closest to the 5 volt rating, either side.

Whenever a small electric item breaks and it is for some reason other than the adapter, I never throw away the adapters. I have a 5 volt, 500 mA adapter. What is yours? If it's a match, send me a pic of your connector end and we'll see if that matches as well. If so, to you it will go.

My adapter has a 2.40mm outside diam. Run yours through the calipers to be sure. I couldn't tell from your post if you were estimating, or had actually measured them.