I work at a professional photography studio and was given the task of creating a photograph that would look good on social media websites. At the same time, the image cannot look good for printing of 5x7+ photos. I just can't seem to find a way to get this to happen in photoshop. They must be something simple that I'm missing. Any ideas?
You simply need to set a low enough resolution. Set the image size no larger than the number of pixels to be displayed in the browser. Screen resolutions are generally lower than print, but it's still going to look "ok" printed by most people's definition even though it will clearly not be professional quality.
To put some rule-of-thumb numbers to it: a print resolution of about 300dpi is required for a high-quality print, but for non-picky print many people will be fine with 100dpi. Below that, even non-skilled viewers will probably object.
So, in order to reduce the image below what might make a great print at 5x7, 1500x2100 pixels is the threshold. That's more than adequate for web viewing on today's computers. To be safe, thorough, you'll need to go below 500x700, which may be a bit small depending on your web use.
That leaves you in the position of explaining to someone that the photo could be printed and probably be okay but not great. Hopefully whoever you have to explain that to will be satisfied, because that's reality.