Yes the perimeter of the remaining part of the square will be same because the square with side 1cm is cut off so as we know all the sides of square are equal so the perimeter of square with side 5cm will have same perimeter as the two sides of small square which were part of big square are gone but the other two sides are added in the perimeter of remaining portion. But now the remaining portion is not square as it has 6 vertices now.