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

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