As you are flying in the ClubWorld cabin you get access to the Galleries Club lounges.

(If you had a BA Gold card or other oneworld Emerald level card you could access the Galleries First lounge, but you don't mention that so I assume you don't).

There is Galleries Club lounge at the North end of Terminal 5, but the main lounge pavilion is at the South end which is where you want to go.

Follow signs for south lounges, when you get there take the escalators up, then up again to reach the Galleries Club South lounge.

The Vancouver flight could go form anywhere.
If it goes from a Satellite i.e. T5B or T5C, then note that T5B has a lounge in it, but you want to go to the main Galleries Club in the south pavilion and spend your time there.

You should also have lounge access in MAN before you fly down.

On the return journey (assume same route), you will get lounge access at YVR, and also access to the Galleries Club lounges in T5 before flying up on the domestic (keep CW boarding pass just in case a problem getting access).