Arnold has plates weighing $5$, $15$, $25$, $35$, or $45$ pounds. He lifts a barbell, which consists of a $45$-pound bar and any number of plates that he has. Vlad looks at Arnold's bar and is impressed to see him bench-press $600$ pounds. Unfortunately, Vlad mistook each plate on Arnold's bar for the plate one size heavier, and Arnold was actually lifting $470$ pounds. How many plates did Arnold have on the bar?

Let's think step by step and output the final answer within \boxed{}.
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