Question 290895
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You only need one negative number to get a negative product,
so just use one -1, and pick 4 positive integers that have sum 18.

Here are four examples:

-1+1+4+6+7=17 and (-1)(1)(4)(6)(7)=-168
-1+2+3+6+7=17 and (-1)(2)(3)(6)(7)=-252
-1+2+4+5+7=17 and (-1)(2)(4)(5)(7)=-280
-1+3+4+5+6=17 and (-1)(3)(4)(5)(6)=-360


Edwin</pre>