For some reason, when things like this crop up, we have a tendency to miss the obvious: Have you asked him why he's crying? At 5, he's mature enough to be able to have a conversation about this. Do it at a time removed from school, not before bedtime, but just out of the blue when you're alone and engaged together. I'd say something like this: "I'm wondering: When you went to preschool, you never cried when I left you, but now, at kindergarten, you cry almost every day. I'm wondering why. What do you think?" Make your tone curious, nothing more.
Maybe he'll say something that may surprises you ("I worry I won't remember where the bathroom is.") and, if you're lucky, something you can easily fix. "Well, that's easy. Let's draw a map!" If it's something less concrete -- "I don't know if I'm going to like it; I don't know if the kids will be friendly today." -- try to find something concrete to help him. With these examples, for instance, you could take a calendar and keep track of days when he has liked it or when he had fun with classmates. Since you know from the teachers that he seems to be happy, the good days will overwhelm the bad ones and that's something concrete for him to see.
Of course, he may not have an answer to your question. Then I'd ask him, "OK, well, maybe you can think about it and let me know what you think. Meanwhile, what can I do to help you so you won't be sad in the morning?" Getting him to problem-solve with you will likely shed some light for you on what might be bothering him.
Something else to keep in mind: Is there something happening at home? Is someone sick? New sib? Job change for a parent or some other issue in a parent's life? One explanation for his behavior might be that he thinks he is "missing out" on something at home, or that he is worried about you or someone else (a grandparent?) and somehow feels disloyal by not being at home. If any of that rings true, I would bring it up: "I wonder if you're thinking about x?" Don't be afraid to name whatever it is. Reassure him in as truthful a way as possible: "Even though grandma isn't feeling well, there's a health aide with her all the time so I know she's ok. I'm going to my job and daddy is going to his job and your job is to go to kindergarten."
Obviously, stay in contact with the teacher! She needs to know this is going on.
Lastly, if you have a conversation and he doesn't have much to say, don't forget the other piece of that -- the how-can-I-help-you question. That's really important because it lets him know that he is part of the solution.