These (and other twist bulbs) are supposed to be great in the long term, from what my EnviroSci instructor said. It requires more cash up front (obviously, $5 per bulb) but they use like 1/4 of the energy and last years if you remember to turn off lights when they aren't in use. Your savings will vary by how much your electricity costs, if you get the bulbs on sale, etc.
I don't have personal experience with them, however, I keep the lights off so often that I'm still using the bulbs that came with the apartment, and my halogen dimmer lamp that hasn't need a new bulb since 1998.
Find out how much electricity other things use as well - heating if electric, appliances, electronics, etc. It'll definitely help your argument if your sibling constantly forgets to unplug a table saw for instance (it's a stretch, but hey).