These are so Eli5 that I would not recommend them for most scenarios, and feel a little insecure with these responses as I am more familiar with the textbook definitions; however, I will take a stab at it. If you are truly talking to a 5 year old:

Watts measure power, or, how quickly you can do work. It's a lot of work to fill a pool with water. Filling a larger pool is more work than a smaller pool. Let's say I have two pumps and a small pool. Both pumps will eventually fill the pool with water, but pump A will fill it much faster. Pump A is a more powerful pump. Pump A is a 100 watt pump, pump B is a 40 watt pump.

Btu measures how much heat I get when I do something. For example, lighting a match might give me 1 btu of heat. Two matches will give me 2 btu of heat. Running the stove for 10 minutes will give me much more BTU than the two matches. Running the same stove for an hour is even more than that. Unfortunately, not all stoves are the same quality. One stove may give me 10,000 BTU in an hour and another stove might only give me 5,000 BTU in an hour.

(There's more kinds of energy than just heat, but BTU typically measures heat, so it's a good place to start if you're new to the concept)