You have until the due date of the return to withdraw the excess contribution plus earnings. However, if there is a 6% penalty, it should be paid from outside funds, rather than from within the IRA.
Thank you for your response. I know the deadline is my filing date. It was helpful to know the 6% comes outside the IRA, but I have to rate this answer as not helpful because your response did not catch a critical error in the advice I was given, and described in my question. i.e., the 6% is paid on the $5000 and not on the money it earned. Someone just sent me an article from the 2011 issue of CPA MAgazine on exactly this topic. It may be of interest.
I'm sorry if you are not satisfied with my answer. You need not ACCEPT if you aren't satisfied.
In some circumstances, though, the earnings withdrawn could be subject to the 10% early withdrawal penalty. That you are required to withdraw them to avoid to 6% penalty doesn't mean they aren't subject to the 10% penalty.