  The article is devoted to optimization of the mean-square approximation
procedures for iterated Ito stochastic integrals of multiplicities 1 to 5. The
mentioned stochastic integrals are part of strong numerical methods with
convergence orders 1.0, 1.5, 2.0, and 2.5 for Ito stochastic differential
equations with multidimensional non-commutative noise based on the unified
Taylor-Ito expansion and multiple Fourier-Legendre series converging in the
sense of norm in Hilbert space $L_2([t, T]^k)$ $(k=1,\ldots,5).$ In this
article we use multiple Fourier-Legendre series within the framework of the
method of expansion and mean-square approximation of iterated Ito stochastic
integrals based on generalized multiple Fourier series. We show that the
lengths of sequences of independent standard Gaussian random variables required
for the mean-square approximation of iterated Ito stochastic integrals of
multiplicities 1 to 5 can be significantly reduced without the loss of the
mean-square accuracy of approximation for these stochastic integrals.
