$P(\frac{5^{th}head}{4\, heads})=\frac{P(5^{th}head\, \cap 4\, heads) }{P(4\, heads)}$
${P(4\, heads)} = (\frac{8}{9}*\frac{1}{2^{4}})+\frac{1}{9}*1$
$P(5^{th}head\, \cap 4\, heads)=(\frac{8}{9}*\frac{1}{2^{5}})+(\frac{1}{9})$
$P(\frac{5^{th}head}{4\, heads})=\frac{\frac{5}{36}}{\frac{3}{18}}=\frac{5}{6}$