I have to say, Rachel said it best. Teach your son that the trash is not a toy - teach him not to touch it at all. With where you are right now, if you just attempt to child-proof, he'll see it as a challenge and put his smart little brain to work on figuring out a way to get into it. You are much better off just teaching him not to touch it at all.
I have a 5 year old and also a 19-month old - we're still occaisionally doing some reinforcement/reminding for the toddler, but, overall they learn very quickly not to touch things you tell them not to. As Rachel said - the trash, the dog's bowls, the houseplants, the entertainment center, the DVD and CD racks, etc...
I didn't want to keep saying "no" all the time, so we've always said "Not for [name]" when they go for something they can't have. We add "YUCKY!" to anything concerning trash. If you can, redirect them to something they are allowed to play with (say "THIS is for [name]" )and get them occupied away from the trash.
Save yourself a lot of grief and teach him this now, and you'll never be the embarrassed woman at someone else's house/the store/a restaurant trying to keep your kid from trashing the place. I've seen it and been very glad it wasn't me!