Question 6
Find the smallest positive integer $n$ for which there exist real numbers $a_1,a_2,\ldots,a_n$ satisfying
$$a_1+\cdots+a_n>0,\qquad a_1^3+\cdots+a_n^3\lt 0,\qquad a_1^5+\cdots+a_n^5>0.$$
$$a_1+\cdots+a_n>0,\qquad a_1^3+\cdots+a_n^3\lt 0,\qquad a_1^5+\cdots+a_n^5>0.$$