Did you know that your question has now also been posted by someone named “hoaihuong” on a different website? :?
I agree with Conchita, the use of can is more informal and is frequently used in situations involving permission. May is more formal. In your sentence, the use of may also sounds formally “parental” to me.
I’d also say that may is more likely to be used in a request. Your sentence sounds like it could be simply a suggestion rather than a response to a request.
But, let’s take a slightly different example (more likely to involve two adults):
You can borrow my dictionary if you like.
You may borrow my dictionary if you like.
The use of may would be overly formal and could therefore possibly sound sarcastic, in my opinion.