If you ever import old photos or videos into Apple Photos and they end up on the wrong date in your photo stream, do not worry! There is a simple way to fix this - the feature is just a bit hidden.
First, click the item you wish to edit in the photo stream. Then click CMD + I to open the info window and double click the date. It looks like this:
In my example, this video is actually shot in 2010 but after importing it to Apple Photos, it shows up under January 2016!
Next, double click the date (where it says 9 January 2016 in the example). A new dialogue will open where you can modify the date and time.
You can also find this dialogue through the "Image" menu although having the Info window open might give you a good clue to what date and time to set, at least in my example when this is revealed by the file name.