∵ 当 x = 1 时,a x ⁵ + b x ³ + c x + 1 = 5
∴ a × 1 ⁵ + b × 1 ³ + c × 1 = 4
a + b + c = 4
∴ 当 x = - 1 时,a x ⁵ + b x ³ + c x + 1
= a × （- 1）⁵ + b × （- 1）³ + c × （- 1）+ 1
= - a - b - c + 1
= -（a + b + c）+ 1
= - 4 + 1
= - 3