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Solution

General term $T_k=\binom{5}{k}(y^2)^{5-k}\left(\dfrac{c}{y}\right)^k =\binom{5}{k}c^k\,y^{10-3k}$. For power of $y^1$: $10-3k=1\Rightarrow k=3$. Coefficient $=\binom{5}{3}c^3=10c^3$.