Remove a working motor from an old broken down washer/dryer at the local dump. Attach paddles to the shaft and set it up so that the stream moves the paddles. You will get electricity out the wires of the motor. You will probably want to regulate the voltage and charge some batteries with it. It will produce potentially way more than 5 watts.

Does that 5watts include transmission losses?

Start scounging old motors. You want ones that ones the include a permanent magnet in them, preferrably in the rotor(centre). these could be anything from simple DC motors to stepper motors(6 wires).

Given the small amount of power you want, it is probably easiest to attach a paddle wheel to the motor shaft and dangle the paddle wheel in the current, then run the heaviest wires that you can back to the light.

If this is going to be a permanent installation, then consider building a more robust floating paddle wheel. Initially something like an old bicycle wheel with paddles attached mounted on two pontoons, or just stake an old bicyle frame in the stream to hold the pabble wheel(paddle size constraints) . If it was a rear hub, then you could use a chain drive, or depending on how you attach the paddles, perhaps a belt drive using some of the modern, very long fan belts (wreck or road side), or even a strip cut from an inner tube.

My guess is that you are going to need to do a lot of fiddling to get useful output, aka, you will want to build the most powerful paddlewheel you can so you can gear up the "generator"

Once you have that built, your biggest problem is going to be transmission losses from the creek back to the kitchen. So much so, that I suggest you look at using a couple of car batteries creek side. charge one for 24hours, whilst the other one provides power for the light, which I assume is only running of an evening..