Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
If you were told it could be installed on 5 computers, I assume you have a subscription, right?
If so, the key is for first time use only. You redeem the key and it is then associated with your Microsoft account, Moving forward your account serves as license.
You can just go ahead and install in this case.
Please go to https://account.microsoft.com/services
Sign in to the Microsoft account you used for the subscription.
You should then see your subscription listed. Find the option called "Install desktop versions of Microsoft 365 apps like Word, Excel and Powerpoint to your devices". It has a down arrow icon next to it.
Click on that. It should start downloading the installer file. Then you just need to run that installer file to install the apps.