Not sure of what to get the 3 younger kids to play. They range from about 3-7.
You're not going to find a game that will be enjoyable for a 3 year old and a 7 year old. A 3 year old will be at the stage of learning how to play a game - i.e. turn order, following simple rules, not winning. Something like Where's my Cupcake? which has zero decisions is good for learning to play games. A 7 year old (and presumably a 5 year old) are unlikely to have that much patience playing with them. These children may be different, but I'm imagining my children playing with a hypothetically 3 year old sibling and I'm fairly sure there would be shouting...
My kids are nearly 5 (son) & nearly 7 (daughter), games they enjoy:
Carcassonne - mainly without farmers but I think they could probably both cope with farmers now.
Hive (Hive Pocket) - my daughter can play with all the standard pieces and can win. My son doesn't understand grasshoppers so we play without them (he can make reasonable moves and occasionally win). I'm not a very good Hive player.
They have played Pandemic, my daughter can play (though wanted to wipe out all the diseases which led to us losing), my 5 year old didn't have the patience and didn't really understand what was going on.