I have $5000 income from contract work. I don't have expenses to claim against the income. Can I use the Deluxe program instead of the Self-Employment income?

Did you receive a tax slip for this income? If you did, then TurboTax Online will make you use Self-Employment, if you have self-employment on a tax slip. But if you don't have a slip, you can enter the income as "Other Employment Income". You can find that page by searching for "tips".