I'm not sure with the following:

(1) What is the order of every Sylow 5-subgroup of $\displaystyle A_5 \times A_5$ ?

(2) Let G and H be arbitrary finite groups. Prove that every sylow p-subgroup of $\displaystyle G \times H$ has the form $\displaystyle P_1 \times Q_1$ where $\displaystyle P_1$ is a sylow p-subgroup of G, and $\displaystyle Q_1 $is a sylow p-subgroup of H.

(3) Find the number of sylow 5-subgroups of $\displaystyle A_5 \times A_5$

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For (1) i think it's 25, as its's 5.5 ?

For (2) I think I use the Conjugacy sylow theorem somehow?

For (3) I think it might be 26 because $\displaystyle A_5 \times A_5$ is simple?

Thanks!