Adobe Photoshop CS5 vs. CC

Thank you very much for your answers!

In this case we'll try with Photoshop CC

Oh yeah, you'll be fine. Like Mike Gondek mentioned there might be some issues with smart objects or things like that,  but you should be fine

is it possible to open content created with Photoshop CS5 in Photoshop CC?

Yes.

Then modify this content, save it and open it again on another computer with Photoshop CS5?

If Compatibility is maximised (Photoshop > Preferences > File Handling) yes, but certain elements (3D Layers, Linked Smart Objects, …) might not be editable.

Also I am not sure when the last new Blend Modes were introduced.

Photoshop is not like Illustrator where you can save as in the latest version 2019 and save down to CS5. The reason is photoshop files are very backwards compatible as most of the data is a pixlel data.

You at worst may experience some issue with newer featurtes such as adjustment layers, or smart objects, but do a test on the CC  computer to ensure.

If you do not have access to CC, then notify the person to avoid using newer features such as smart objects which  might not be compatible.