I purchased Photoshop C5 in 2011. My old desktop computer, with Photoshop C5 has had to be replaced. Is there any way to install Photoshop C5 either my MacBook Mac OS X 10.6.8 or on my new desktop computer, an HP with Windows 8.1 64-bit? I am gathering no, but can tell me how, that would be great. :-)
Your Photoshop CS5 license will only work on the platform (Mac / PC) you originally licensed it for. If your old desktop was a Windows system, there's no reason you shouldn't be able to use your serial number to activate it on your Win 8.1 system.
If you've used up both your allowed applications, give Adobe Customer Support a call. Explain that your old system is long gone and they should be willing to reset your usage count for you so you can put the software on the new machine.