K.D.
My son was the same at 5. Finally near his 6th birthday we enrolled him in Karate. He loves it. (He asked for karate nearly continuously from 5 to almost 6).
Before you sign him up, attend a few classes at various studios, talk to the instructor about their philosophy, ask about total costs (uniforms, tournaments, etc), and then decide on a studio. We live in a small town, so options were limited, but we still had 3 studios to choose from. The instructor should be geared toward younger children and ready to provide the extra help and support younger kids require.
It has been a great experience for my son so far -- enough that I would recommend it to others as well.