Can I use 5 different accounts with TurboTax desktop?

No.    You can download the software to five of your own computers if you want to, but they all must be under the same account.  That is how they are enforcing the rule---you cannot just give your license key to other people to use the software.    All of the downloads for your license key must be on your own account.

With the desktop version, you can create many tax returns but only 5 can be e-filed, If you want to file tax returns for you, kids, parents, all from your purchase, you can do that for them.