A worker is paid according to the number of days he works and the number of hours he works each day. He works for 5 days, and each day he works 2 hours more than the previous day, starting with 4 hours on the first day. If he is paid $15 per hour, what is his total payment at the end of the 5 days? Let's think step by step and output the final answer within \boxed{}.
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