FINAL Conclusion

Five where needed to unlock
Five where needed to complete
Only one holds the lock
and only then comes defeat
Part 1 & 2 of Relic has ingame evidence they are linked with Coil 1 & 2
Part 3 holds the key to 5 in Relic Quest, same happens in Coil 3 to 5

Extra Backup Motivation

When I was a kid, my mum told me this:

One day

You'll walk on the ground.
Swim in the water.
Fly in the air.
Turn 5 - Tornado is a Wind Ability.
Turn 3 - Completion by "flying in the air"

Air = Wind
Completion in 3 because of Wind = Completion in 5 because of Wind.