Number of $5$-card hands where all $4$ suits are present

Question

A standard $52$-card deck consists of $4$ suits and $13$ ranks. Find the number of $5$-card hands where all $4$ suits are present.

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I tried to solve it like this:

   _    _    _    _    _
 13c1*13c1*13c1*13c1*48c1

ps* _ represent cards. Why is my approach wrong in this question?