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A paralallogram with a perimeter = 13 units can be made to "lean" over until its area becomes 5 square units.

Also:

A rectangle with a long side of 5.608495283 and a short side of 0.8915047169 will have a perimeter of 13 units and an area of 5 square units.

Also:

An isosceles triangle with say 2 legs of 5.5943 and the 3rd leg of 1.8114 will have a perimeter of 13 units and an area of 5 square units.

So the answer is that there are many shapes that will satisfy the perimeter and area given.

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