PS CS5 can only use up to ACR 6.x, its just not possible to upgrade to ACR 8.7.
If you are sending raw files from Lightroom 5 to PS CS5 for further editing when you see the mismatch warning choose "render using Lightroom" if you use the option "open anyway" the ACR version may not be able to process all your Lightroom edits.
The latest version of LR 5.7.1 is the equivalent of ACR 8.7.1
Thanks for your reply. It seems bizarre that the warning message tells me to upgrade yet that is not possible. Do you know why Adobe have not addressed this?
Sure it's possible; upgrade to PSCS6. Adobe never promised you endless free updates, only for the support lifetime of PSCS5. And after PSCS6 you won't even be able to upgrade to a new perpetual license.
Thanks for your reply elie-d. I wasn't complaining about the "lack of endless free updates" as I realise that is not reasonable to expect. I am however annoyed that an error message should tell me to do an upgrade to CR 8.7 when I gather this is not possible. I wasted ages looking for a way to do that. If the error message was correct then that would have saved me a lot of time.