S.K.
C.,
5 year olds can definitely handle clearing their own dishes and getting them in the dishwasher. They can also get dirty clothes into the laundry basket and put clean clothes away in the drawers. They can sort colors (supervise this one) and load and unload the dryer (and washer if it is a front load.) My 5 year old just got to the point where he can fold clothes nicely. He can make his bed and keep his room clean.
Recently my 5 year old has taken on vacuuming, sweeping and using the dust buster. He really likes these jobs, doesn't even consider them chores.
When the weather warms up, he can help with gardening - planting, watering and weeding with supervision (my kids still get the weeds mixed up sometimes.) In the fall he can bag leaves.
I see you have a 1 year old. He should be able to get diapers and wipes for you, throw away dirty diapers and put the wipes box back. He can also help clean up baby toys. I know some people think that older siblings shouldn't be asked to help with younger ones, but I disagree. I explain that we are a team and we all chip in and help out. I cleaned up my big kids baby toys for them and I still do a ton for them, they can help out someone else, too.
I don't have my kids do these jobs exclusively or keep track with any kind of a system. Maybe I should, I don't know. When it is time to get something done, I just rally the troops and we all work together until it is done. Then it feels like we are a team and doesn't have that "supervisor / worker" feel to it.
Good luck,
S.