#### Answer

First Derivative: s' = 15$t^{2}$ - 15$t^{4}$
Second Derivative: s'' = 30$t$ - 60$t^{3}$

#### Work Step by Step

Using the power rule:
Work with the first and second term separately
First Derivative:
s = 5$t^{3}$ - 3$t^{5}$
s' = (3)(5)$t^{2}$ - (5)(3)$t^{4}$
s' = 15$t^{2}$ - 15$t^{4}$
Second Derivative:
s' = 15$t^{2}$ - 15$t^{4}$
s'' = (2)(15)$t$ - (4)(15)$t^{3}$
s'' = 30$t$ - 60$t^{3}$