  In previous papers, we discussed the recurrence relations of the
multi-indexed orthogonal polynomials of the Laguerre, Jacobi, Wilson and
Askey-Wilson types. In this paper we explore those of the Racah and $q$-Racah
types. For the $M$-indexed ($q$-)Racah polynomials, we derive $3+2M$ term
recurrence relations with variable dependent coefficients and $1+2L$ term
($L\geq M+1$) recurrence relations with constant coefficients. Based on the
latter, the generalized closure relations and the creation and annihilation
operators of the quantum mechanical systems described by the multi-indexed
($q$-)Racah polynomials are obtained. In appendix we present a proof and some
data of the recurrence relations with constant coefficients for the
multi-indexed Wilson and Askey-Wilson polynomials.
