I have a felony 5 on my record and want to get a passport and then a visa for South Africa. The criminal offense is in the United States and happened 5 years ago. Will I be eligible to get a passport and, separately, a visa to enter South Africa?
Yes, you may be able to get a US passport, and, yes, it may not prevent you from entering South Africa. It will depend on your circumstances.
According to U.S. Law 22 U.S.C. 2714, the government won't issue a passport for those with drug offense convictions, either Federal or State charges, and when the crime was committed while crossing an international border. This disqualification remains during imprisonment and during parole.
The U.S. Secretary of State has the discretion to disqualify a convicted felon if the charge is a misdemeanor Federal or State drug charge. There may be an exception when a misdemeanor drug charge involves the first offense possession of a controlled substance.
Form DS-11, the Application for a U.S. Passport. doesn't ask about criminal history, although not disclosing information that could make one ineligible could trigger a revocation.
In some instance, sentencing, probation, or parole terms may deny a person the right to a passport. Other reasons that a passport may be denied include being arrears on child support, or having an outstanding arrest warrant (these don't include parking or civil infractions).
After overcoming these hurdles and getting a passport, the next step is entering another country. US passport holders have the privilege of entering many countries visa free, including South Africa.
U.S. citizens (U.S. passport holders) visiting the Republic of South Africa for ninety (90) days or less for tourism / business purposes do not need visas.
However, you may decide to apply for a visa to avoid any potential challenges or issues on entry or while in the country. The visa application Form BI-84 does ask
Have you every been convicted of any crime and any country?
Is a criminal action pending against you in any country?
The South Africa Immigration Act stipulates that anyone who has a previous criminal conviction may be declared an “undesirable person” and the Act considers failing to disclose prior convictions as "deception by silence."
In any event, you have certain challenges. You may wish to arrange an email or Skype consultation with a member of the Law Society of South Africa to determine whether you are admissible and whether you would need to apply for pre-clearance prior to travel.
Afterwards, consult with the South African Consular Civic and Immigration Services North America.
Also review this TSE question which posed a similar question.