Are you talking about the number of tax returns that can be filed with the desktop TurboTax software, or the number of TurboTax Online users? The tag below your question says you are using TurboTax Online. Is that correct?
You can have up to 5 TurboTax Online accounts with the same email address. If you need more accounts you have to use a different email address.
With the desktop TurboTax software you can e-file up to 5 federal tax returns. That limit is set by the IRS, not by TurboTax. There is no way to increase the limit. You can prepare additional tax returns, but they have to be filed by mail.