When I turn on the cold water tap in the kitchen sink, I get cold water for 5-10 seconds, then only a dribble until I turn it off. After waiting a few seconds, the cycle repeats. This is a single handle fixture. The hot side works normally.

Sounds like something is clogging up the faucet. Have you tried taking it apart and seeing what is in there? Could be some built up dirt.

The Twink nailed it. Some trash got in your valve and needs to be flushed out.
Before we can continue I need more information. 'm assuming that you have a two handle sink faucet and not a one handle faucet. Correct? Has it got a sprayer? What brand is it? How old? Let me know, Tom

Yes I agree with Twinkiedooter, Close the angle valves under sink, Remove the handle and the cartridge now open the angle valve one by one slowly and have a pan on top of the valve to catch the water when both sides are flushed, install the cartridge, try and see if your problem is fixed, good luck.

John

Sorry Tom I was typing at the same time, Thanks.

John
No problem John, Great minds think alike!