Originally Posted by NWIFlyer

I think we may need to manage the OP's expectations a little here to avoid disappointment, because none of these things are possible.

The VIE flight will leave from T3. That means there is no access to the real airside bit of T5 (the OP would be rejected at security) so the CCR is out.

So, too, is access to the F side of the CX lounge at T3 - the OP's departing flight will be in CE, so only J side will be allowed. The ability to use a higher than normal departure lounge is due to BA's more generous lounge policy, but it only applies to their own lounges - so the OP could presumably access the T3 BA F lounge on the back of their incoming F boarding pass, but not a F lounge operated by another carrier. I imagine that also precludes pre-booking a treatment at the Elemis spa in T3, because the VIE flight isn't long haul.

If a treatment is desired, then the only option is at the spa in the T5 arrivals lounge.