  The article is devoted to construction of effective procedures of the
mean-square approximation for iterated Stratonovich stochastic integrals of
multiplicities 1 to 5. We apply the method of generalized multiple Fourier
series for approximation of iterated stochastic integrals. More precisely, we
use multiple Fourier-Legendre series converging in the sense of norm in Hilbert
space $L_2([t,T]^k),$ $k\in\mathbb{N}.$ Considered iterated Stratonovich
stochastic integrals are part of the Taylor-Stratonovich expansion. That is why
the results of the article can be applied to implementation of numerical
methods with the orders 1.0, 1.5, 2.0 and 2.5 of strong convergence for Ito
stochastic differential equations with multidimensional non-commutative noise.
