5:20a Therefore we are ambassadors for Christ,

So, we (excl.) are ⌊official⌋ messengers of Christ,
-or-
So then, Christ commissioned us to act on his behalf,

5:20b as though God were making His appeal through us.

and God urges ⌊people⌋ ⌊to accept his message⌋, using us to speak for him.
-or-
indeed, God himself invites/exhorts ⌊people⌋ ⌊to believe⌋, by having us speak on his behalf.

5:20c We implore you on behalf of Christ: Be reconciled to God.

We (excl.) plead on the behalf of Christ: Let God reconcile with you (plur.).
-or-
As those speaking for Christ, we urge this: allow God to restore his relationship with you.

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