Turn in bounties immediately in the character that you are focusing on first. Each day, log in on your two alts to pick up the dailies and hold on to those. By the time your first character is rank 5, your other character each have like 9 green bounties and then the weeklies as well. Play a few games on the alts on Sunday/Monday, turn in the bounties, they'll be rank 5 no problem.
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That seems to be what most people say to do, I'll probably do that this time around