If CS5 work at all for you in an up to date system, count your blessings and don't mess with it. Plan for the day you will need to get a subscription instead.
Did you read what it said?
Error downloading, not installing, check your connectivity...
Yes, I read it. Older apps are finding it harder to connect for a variety of reasons including tightening up security, and just general weirdness in something Adobe haven't supported in forever. My reply stands: don't mess with it. You could lose it all.
My reply was to the OP (no grey indented box).
With your newer Windows OS running, there is no guarantee that CS5 updates will be able to install.
You can try by making sure you are running as an Admin account.
If you truly wish to keep CS5, don't upgrade your OS and stay on the last build that ran for you. Attempting to update either OS or CS5 runs the risk of breaking beyond recovery.
You can also check your account on Adobe.com to see what available downloads you have but your issue may not be downloading, the issue could be installing on an incompatible OS.