How was Gideon V. Wainwright not a violation of the 5th amendment?

The precedent set by the precursory case of Betts v. Brady was overturned, thus giving Gideon a chance to have his case re-heard with appropriate counsel.

He did not self incriminate himself because the standing law at the time was that each case was evaluated as to it's need for court appointed counsel. When the attorney general denied his crequest for an attorney thee left no other option; therefore, the man had no choice but to represent himself.

It's a wonderful with many different legal aspects involved.

Since his first conviction was overturned on constitutional issues, there was effectively no trial (a mistrial of a sort) - so no double jeopardy. If he was tried and found innocent, he couldn't be tried again on the same charges. Right to counsel is now guaranteed if the possible sentence includes confinement. That's why traffic court (minor civil violations) don't get you an attorney unless you want to hire one at your expense.