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Alternating Euler sums and special values of Witten multiple zeta function attached to so(5)

In this note we shall study the Witten multiple zeta function associated to the Lie algebra so(5) defined by Matsumoto. Our main result shows that its special values at nonnegative integers are always expressible by alternating Euler sums. More precisely, every such special value of weight w>2 is a finite rational linear combination of alternating Euler sums of weight w and depth at most two, except when the only nonzero argument is one of the two last variables in which case $ζ(w-1)$ is needed.