You are terrific! What a difficult job you have with all those kids. Is the 5 yo boy a foster boy? If so the lying may have much more complicated reasons than what my thoughts below address. I would recommend getting him into counseling. I've been a foster mom and the state paid for counseling for my foster child.
I think that there are many reasons for children that young to lie. For one thing they are in the process of learning about their world and their brain is still developing. Lies do not have the same meaning for them as they do for us. Lying is common during the preschool years. I do think that if you don't make a big deal of it and learn how to handle it in a way that doesn't put down the child the child does outgrow it.
My granddaughter, who is 3 is doing a lot of lying according to my daughter. But what I see her doing is telling stories of how she would like it to be. I see her mother getting quite upset not only at the lying but at all the other misbehaviours of a normal 3 yo. When she asked my granddaughter why she was lying she said that she didn't want to get in trouble. My daughter handles it by telling her that she won't get in trouble if she tells the truth but that is not always the case. My granddaughter knows that Mama will be unhappy with her anyway because she did misbehave. Kids are quite perceptive.
I recommend, first of all not setting up the child to tell a lie. If you know what the truth is, state it. If you know they broke the toy on purpose for example don't ask, who broke this toy or even how did this toy get broken. Say, because you broke this toy your consequence is.......If the toy was broken by accident, be sympathetic about the broken toy. If you don't know if it was on purpose or not have a conversation about it in a neutral way, not accusing the child of misbehavior and thus allowing him to tell the truth. The important thing here is to be calm, matter of fact, and non accusatory.
Remember that when the child misbehaves, even when he's lying, he is still Ok. Reinforce the good behaviour and treat him with respect when dealing with the bad behavior. And most of all relax. it is normal for kids his age to lie.
I look at noticing a lie as a teachable moment. As you've found punishment doesn't work. what is most important is teaching your son the difference between a lie and the truth and the appropriate way to use fantasy. I'm not saying ignore the lie. I am saying acknowledge it by saying you know it's not the truth and the truth is important and then deal with whatever had originally happened. If you don't know for sure if it's a lie or not you can even say that you don't know and that you'd like him to tell you the truth but don't make a big deal of it. Deal with what happened. Because young children are still learning focus on the teaching.
It has been my experience as a parent and grandparent that the more I focus on negative behaviour in a negative way the more I get negative behaviour. And the more I can be calm and matter of fact (avoiding anger) the more effective I can be. I know it's difficult to do that but it's essential.