Solve a_{5}=1/w_{0}=1/a_{2as_{4}}

$$a _ { 5 } = \frac { 1 } { w _ { 0 } } = \frac { 1 } { a _ { 2 } a s _ { 4 } }$$

Evaluate (complex solution)

$$a_{5}=\frac{1}{w_{0}}\text{ and }\frac{1}{w_{0}}=\frac{1}{aa_{2}s_{4}}$$

Solve for w_0

$$w_{0}=aa_{2}s_{4}$$

$$a_{2}\neq 0\text{ and }a_{5}\neq 0\text{ and }a\neq 0\text{ and }s_{4}=\frac{1}{aa_{2}a_{5}}$$

Solve for s_4

$$s_{4}=\frac{w_{0}}{aa_{2}}$$

$$a_{5}=\frac{1}{w_{0}}\text{ and }a\neq 0\text{ and }w_{0}\neq 0\text{ and }a_{2}\neq 0$$