He is definitely trying to get attention. I think he is jealous of the baby and when he goes to school he is afraid that you will leave him there because of the baby, he probably feels like he is not as important as he use to be. Give him a lot of love and praise, remind him that you can't wait til he gets home from school and tells you all about it. Spend some time with just him, maybe when the baby is taking a nap. Kids need to be reassured that they are loved. I hope it works for you.
Oh, I hate school troubles!!! It is so frustrating and you know he isn't happy either when it gets to that point. I'm wondering if he had any preschool experience. Kindergarten can be a huge transition for little guys (and 5 is still little). They have a lot of demands on them that if they aren't use to them, kids have a tough time. I'm a stay at home mom too and although my kids went to preschool, it was only for a few hours a day three mornings a week. That is why I was so happy they have half day kindergarten in our school district. Do you have that option? It might be a better fit for him if they offer it.
Having a sibling at home can make kids a little jealous. My son that is in kindergarten now is fine this year in kindergarten but we had some rough preschool experiences. I always made sure I didn't go on and on about how much fun little brother and I had. I acted like we just sat and did nothing the whole time he was at school. I will say that in my opinion, usually a child is very unhappy inside if they are behaving well at home but having issues in school. So try to be empathetic to him.
As far as in class, sitting him right by the teacher at circle and throughout the day is helpful. Have her make him her "helper" when she can. Ask her about social things going on with the other kids and if this is a problem area, she could maybe facilitate with this. Maybe she could chart what happens before the flare ups. Maybe you could volunteer in the class if you have someone to watch your baby for a day (or even a couple of hours). Make sure he gets physical activity throught the day as well---- do not let a teacher punish him with taking recess away.
Good luck; hopefully it well get better soon.