Bob spent $95.08, including $5.38 tax for five books for his children. The price of each book is the same. What is the price without tax of each book?

Let X be the price without tax of each book.

So Bob spent 5 * X + X * 0.0538 = $<<5*X+X*0.0538=95.08>>95.08 .
So 5.0538X = $<<5.0538*X=95.08>>95.08.
So the price without tax of each book is X = $95.08 / 5.0538 = $<<95.08/5.0538=18.82>>18.82. Answer: \boxed{18.82}.