Office 365 – Can Home Premium Be Used on a Business Computer?

Microsoft's licensing requires each user to have their own license regardless of the number of devices on which they activate the software.

According to the Microsoft Online Services Terms^* which includes licensing terms for Office 365 Applications, a subscription license ("User SL") is required for each user:

A User SL is required for each user that accesses the Online Service unless specified otherwise in the Online Service-specific Terms.

^{source: Microsoft Online Services Terms, page 4}

The "Online Service-specific Terms" are found later in the document and confirm individual users are granted five concurrent software activations:

Each user to whom Customer assigns a User SL must have a Microsoft Account in order to use the software provided with the subscription. These users:

• may activate the software provided with the SL on up to five concurrent OSEs for local or remote use;
• may also install the software, with shared computer activation, on a network server or Microsoft Azure Platform Services and use the software to create, edit, or save documents. For the purpose of this use right “network server” means a physical hardware server solely dedicated to Customer use. This shared computer activation provision does not apply to Customers license for Office 365 Business; and
• must connect each device upon which user has installed the software to the Internet at least once every 30 days or the functionality of the software may be affected.

^{source: Microsoft Online Services Terms, page 19}

^{*Also available from the Microsoft Volume Product Licensing site}

Yes you can sign up for and use the business and enterprise subscription plans. They are just more expensive than the O365 for home use and cover different use cases, products, and have an SLA.

O365 for home uses Skype and OneDrive personal

Business / Enterprise plans leverage Lync and OneDrive for Business, and you need the more expensive plans to access the full Desktop/Mobile clients for Office.

As for the 1 user / 5 pc - this is tied to the Office 2013 pro plus installations. It means you can activate Office on up to 5 machines with each valid license. When in O365 you can manage where these are activated. It's very common today to have a work, home PC, and mobile device activated for use, and potentially a temporary location as well.