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. And you can't buy another Desktop program to get more efiles.
See if one of them can use the Online Free Edition or use the IRS direct file or one of the other free files listed at the IRS.
IRS Direct File
https://directfile.irs.gov
IRS Free File partners
https://www.irs.gov/filing/irs-free-file-do-your-taxes-for-free
