would you climb all the way to 5000 feet on the edge of the blue line in a twin?
No.
I can't see why anyone would want to climb at Vyse (blue line) when Vx (all engines operating) would be the appropriate speed under normal circumstances.
Regarding initial climb speed? This would depend on the circumstance. A departure from an aerodrome where the LSALT for the route is 5000', the answer would be to climb at Vx to 5000'.
Once terrain clearance has been made, accelerate to the desired en-route climb speed.