The 5mm measurement of a diamond is at the girdle. A round diamond with this measurement weighs between .40 and .50 carat. An emerald cut, princess cut or other cut will have a different measurement or series of measurements.
Depending on the cut of the diamond, the 5mm space may or may not 'fit'.
The size of these two objects is exactly the same: 5mm.
A one-half carat diamond, in a round brilliant cut, measures about 5.2MM at the girdle.
If the diamond is an ideal emerald cut with these measurements, the diamond may weigh about one quarter of a carat. Otherwise, you have stated the diamond's 'big' size in measurements.
Both Asscher cut and Princess cut diamonds have at least one measurement that is 5mm, and both with this perimeter weigh in the one carat range. ('Square' diamond is a description for a rather generic cut.) A certified gemologist can give you an exact weight for your diamond.
You're attempting to determine the weight of a stone given its measurements, which can not be accurate, since the two units of measurement are different. Roughly, however, if the stone is round, it may weigh between .40 and .50 carat, if the 5mm measurement is at the girdle of the diamond.
This stone may be in the .50 carat range, but a gemologist can weigh the stone for you and give you the carat weight.
Carats and millimeters do not correlate directly. If, however, your question is about a gemstone cut as a round brilliant gem, it may weigh between .40 and .50 carats or 40/100ths or 50/100ths of a carat. Take your gemstone to a jeweler whom you trust and ask that the diamond be removed from its setting and weighed. That is the only way to know the exact weight of any gemstone.
5mm :)
5mM
25mm2 = 5mm * 5mm
5mm is half a cm
5mm wide