This is a typical separation problem: seven white balls will separate 5 black balls.
The seven white balls create eight places to place a black ball:
\(\displaystyle \underline{~~~~~}w\underline{~~~~~}w\underline{~~~~~}w\underline{~~~~~}w\underline{~~~~~}w\underline{~~~~~}w\underline{~~~~~}w\underline{~~~~~}\)
Choose five of them \(\displaystyle \dbinom{8}{5}.\)
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