$$5a(a + b + c) - 5b(a - b - c) - 5c(a + b - c) = 5a^2 + 5ab + 5ac - 5ab + 5b^2 + 5bc - 5ac - 5bc + 5c^2 = 5a^2 + 5b^2 + 5c^2 + (5ab - 5ab) + (5ac - 5ac) + (5bc - 5bc) = 5a^2 + 5b^2 + 5c^2$$