VN-TST 2015 Problem 6

Find the smallest positive interger number $n$ such that there exists $n$ real numbers $a_1,a_2,\ldots,a_n$ satisfied three conditions as follow: a. $a_1+a_2+\cdots+a_n>0$ ; b. $a_1^3+a_2^3+\cdots+a_n^3<0$ ; c. $a_1^5+a_2^5+\cdots+a_n^5>0$ .