It really depends on the kid. My 6-year-old isn't really ready. She enjoys her Junie B books but wants the whole book read or wants to start at the beginning every time vs picking-up where we left off. And she hasn't showed any interest in any of the other chapter books I've shown her.
The Junie B series is well recommended but has a girl as the main character. Some boys aren't interested in stories about girls. Some parents also object to the bad grammar. The stories are told in Junie's voice and she talks like the 5-year-old she is.
I've also heard good things about the Magic Treehouse series.
We recently discovered Minerva Louise. She's a chicken who gets confused about how the people world works. Kids this age find her very funny. As a sort of chapter book test, you could check out 3 of her books from the library and read one each night. They aren't sequential, but you can see how you son takes to visiting the same character several days in a row.
the Frog and Toad books (or is there just one?) would also be a good test. Short stories in one book that are about the same characters but aren't sequential. Start looking in the early reader section of the library. Those books are easy to read, tend to rhyme and often tend to be broken into chapters.