Yes, your child has grown up now, but he's still very attached to you and that attachment can often come out in forms of separation anxiety. It is a common problem that most kids have around the age of five years. With more time spent in school and in other activities, there are more goodbye than hellos.
What you need to know
A kid who has been in a cocoon all this while, suddenly feels insure with this sudden change. Needless to say, his whole world crumbles down, and here you have a child who is extremely cranky, throwing tantrums, making up stories to get out of school, being unruly, etc.
As a parent, this is a tough situation and you are bound to get hassled. A little bit of planning and patience can help you and your child sail through this rather easily. Understand the change the little kid is going through. Access him from this point of view and everything will look normal. Speak to your child in advance about this impending separation. Don't let it come as a shock. (For eg: From next week Ryan is going to school. And we will be a big boy and will make friends etc.)
What you can do
Allow your child to emote and express his feelings. Tell him that this separation is temporary and you are all going to meet soon. Ensure that you keep the goodbyes simple, the more you fuss around, the more the child finds it difficult to accept it as a normal thing. Separation is difficult for everyone. But for a child it is more because it is a new happening for him. Be patient and prepare well, you and your kid will sail through these teary times peacefully.