If I move Shadow Order Disciple, can I burn 5 to add +5 might?

No. You can only pay Burn 1 once per trigger — one move, one Burn, one +1 Might.

Shadow Order Disciple's ability is a triggered ability with a cost within instructions (Rule 742.1.b): "When I move, you may [Burn 1] to give me +1 [S] this turn." When the trigger resolves, you choose whether to pay the single Burn 1 cost or not. There's no mechanism to multiply that cost or pay it multiple times from one trigger — it's a binary decision.

To get +5 Might, you'd need the Disciple to move five separate times, triggering the ability each time.