If you absolutely must have genuine Microsoft Office locally installed on macOS 10.10.5:
Office 2016 was the first suite designed with the Retina display and ribbon interface that modern users recognize. It includes: Microsoft Office For Mac 10.10 5 Free Download
To directly answer the query :
If you need Office specifically for work or school, check if your institution provides a free or discounted license. Otherwise, consider upgrading your Mac or using the free alternatives listed above. If you absolutely must have genuine Microsoft Office
A: No. The installer will reject the OS immediately. contains no malware
LibreOffice is the most recommended. Download the legacy version (6.4.7) from their official archive. It will never expire, contains no malware, and handles Microsoft’s file formats better than any other free alternative.