Pascal's Triangle and Binomial Coefficients

We want to compute some binomial coefficients knowing the values

$${{5}\choose{0}} = 1$$ $${{5}\choose{1}} = 5$$ $${{5}\choose{2}} = 10$$ $${{5}\choose{3}} = 10$$ $${{5}\choose{4}} = 5$$ $${{5}\choose{5}} = 1$$

If we want to evaluate ${{9}\choose{4}}$ by repeatedly using Pascal's Identity until the expression is only in terms of the six binomial coefficient evaluations above, what is the smallest number of times must we use Pascal's Identity?