The 5 efile limit is from the IRS. It's to prevent fraud and people filing fake returns. To do more you have to sign up as a ERO - Electronic Returns Originator and be an authorized E-file provider. https://www.irs.gov/e-file-providers/become-an-authorized-e-file-provider
Maybe you can use the Online Free Edition to file for someone? Or the IRS Free File, it can do more than the Turbo Tax Free Edition.
https://www.irs.gov/filing/free-file-do-your-federal-taxes-for-free
