Volume = 480cm

Let the length of any side of the original sqare piece of metal = x.

Length = x-5

Width = x-5

Height = 5

You really have to picture this, try drawing it out.  When you cut out 5*5 squares, and fold up the sides, the height wil equal 5.  The length and width are x-5 because you are subtracting 5 from each side of a square.

Volume = l*w*h

Substitute in the above values and solve for x

480=(x-5)*(x-5)*5

96=(x-5)(x-5)

96=x^2 - 10x + 25

0 = x^2 - 10x - 71

Use the quadratic formula to solve for x.

x = -b +/- (sqrt(b^2-4ac))/2a

a:1 b:-10 c:-71

x = (10 +/- sqrt(100-(-284)))/2

x = (10 +/- sqrt(100+284))/2

x = (10 +/- sqrt(384)/2

x = (10+19.6)/2 or x= (10-19.6)/2

Choose the first because the dimensions have to be positive:

x = 14.8.  The dimensions are approximately 14.8 cm by 14.8 cm

*The wording in this problem is confusing: IF THIS IS NOT WHAT THE PROBLEM IS ASKING FOR, MESSAGE ME AND I WILL REDO IT OR REFUND YOU :)