Upgraded to LR5.7 and PS Elements 13. Using a Solid State Drive which is becoming Full! Can I remove older versions of these programs without affecting the functionality of the new programs?
Yes, there is no need to keep previous versions of software on the SSD (or on your computer).
Also, you didn't mention this but if the photos are on the SSD, you should move them off the SSD to a regular hard disk using these instructions: Adobe Lightroom - Find moved or missing files and folders
Thank you that will help clear some space. Fortunately my photos are on a large separate disc with external back up.