3rd class medical now expires in 60 months ?

There is no "student's certificate" for sport pilots, just
endorsements in the logbook (i.e. to solo, to fly in certain
airspaces, etc).

Rocky, I believe that there is a requirement for a Student Pilot
Certificate.
http://www.faa.gov/licenses_certific...0_guidance.pdf

In addition to the log book endorsements you mentioned and listed in the
above document.
The "Student Certificate" can be issued by the FSDO or a Designated Pilot
Examiner. It may have a restriction that it is to be used for "Glider,
Balloon, or Light Sport Aircraft Only" as it is not backed by a medical
examination. If the Student Pilot does not have an appropriate form of
showing medical requirements are met for Sport Pilot, then it will be
restricted to Glider or Balloon.

"An applicant for student pilot certificate for sport pilot -

Must hold either a medical certificate or U.S. driver's license -- A person
must hold and possess

either a valid medical certificate issued under part 67 or a current and
valid U.S. driver's license when

exercising the privileges of a student pilot certificate while seeking sport
pilot privileges in a light-sport

aircraft other than a glider or balloon.?