The answer is: 4.00 mol of Fe(OH)2 is produced.
Balanced chemical reaction:
Fe(s) + 2NiO(OH)(s) + 2H₂O(l) → Fe(OH)₂(s) + 2Ni(OH)₂(aq).
n(Fe) = 5.00 mol; amount of iron.
n(NiO(OH)) = 8.00 mol; amount of nickel oxide hydroxide, limiting reactant.
From chemical reaction: n(NiO(OH)) : n(Fe(OH)₂) = 2 : 1.
n(Fe(OH)₂) = 8 mol ÷ 2.
n(Fe(OH)₂) = 4 mol; amount of iron(II) hydroxide.