= Solution
Multiply the convergent <Taylor series> $\cos x=1-x^2/2+x^4/24+\cdots$ and $\sinh y=y+y^3/6+y^5/120+\cdots$. Keeping all terms through total degree five gives
$$
\boxed{\cos x\sinh y=y+\frac{y^3}{6}-\frac{x^2y}{2}+\frac{y^5}{120}-\frac{x^2y^3}{12}+\frac{x^4y}{24}+O((|x|+|y|)^7).}
$$
There are six nonzero <monomials> displayed, so the answer does not select only part of the tied total-degree-five terms when asking for at least four terms. Both original series converge for every finite real $x,y$.
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