Find all real numbers aaa for which there exist non-negative real numbers x1,x2,x3,x4,x5x_1,x_2,x_3,x_4,x_5x1,x2,x3,x4,x5 satisfying the relations
∑k=15kxk=a,∑k=15k3xk=a2,∑k=15k5xk=a3.\sum_{k=1}^{5}kx_k=a,\quad\sum_{k=1}^{5}k^3x_k=a^2,\quad\sum_{k=1}^{5}k^5x_k=a^3.k=1∑5kxk=a,k=1∑5k3xk=a2,k=1∑5k5xk=a3.