5-term to 3-term recurrence relation

Question

I have a 5-term recurrence relation of the form: $$\alpha_n a_{n-3} + \beta_n a_{n-2} + \gamma_n a_{n-1} + \delta_n a_{n} + \rho_n a_{n+1} =0 .$$ How can I rewrite this, as a 3-term recurrence relation? i.e. how to rewrite in the form $$\bar{\alpha}_n a_{n-1} + \bar{\beta}_n a_{n} + \bar{\gamma}_n a_{n+1} =0$$.