Not in a strictly expected value sense, no. It's never going to be a rational choice from an financial point of view (i.e. there is always something else you can do with the $5 with better expected returns).
But if you get some other value out of it you place at least $5/wk utility on, sure. Maybe you get more utility out if it than a movie a month, or whatever.
I'll buy the occasional $10 scratcher, and then wait like a week to scratch it all off. The $10 is worth getting to ponder what I'll do with my massive windfall for that week!
Already maxing my ROTH and 401K so I figure it's like $80 a year well spent to entertain the phantasy.
That depends on the probabilities involved. If you send me $5/week, I might decide to give you $10 million one day. I don't have $10 million and I don't think I would want to give it away if I got that kind of money, but it could happen. Are you interested? Do you think anyone would be?
What if $5 per week for the rest of their life doesn't impact an individual's standard of living, but $10 million would drastically improve it?
Does it then make (more) sense to participate?