Yes if those contacts are bridged you only need to connect one pair. Separating them by removing those bridge pieces allows 'bi-wiring' and 'bi-amping' which are rabbit holes you really, really don't need to go down at the moment!
FWIW I take the view that if 'speaker cable is the best to use for a 5 metre run' then it's probably best for a two centimetre one - so this is how I've done mine. Though expect howls from somebody!
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On the bluetooth front, I have one of these and it's perfectly serviceable though I use it mainly for Internet radio, which it is very good at. I got mine off FB marketplace for eighty quid:
www.majority.co.uk
These seem to have a thing for the DAB functionality breaking so don't rely on that aspect if buying SH.
There are quite a few bluetooth receivers around though as you've obviously seen browsing amazon. The main recommendation would be when you see something always google '{name of thing} review' before you buy. Buying from Richers is always a sound (fnaagh fnaagh) choice as they would normally take something back if you don't like it, provided you haven't broken it or thrown away the packaging.
https://www.richersounds.com/mee-audio-af-ch-connect-hub-dual-bt-transmitter-receiver/
Have fun!