Question 1012875
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If you mean the difference between length and width 
is at least 5 cm (not 5 meters as you posted), then:
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L=length; W=width
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P=2(L+W)
19=2(L+W)
9.5=L+W
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L-W=5
L=5+W
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9.5=L+W
9.5=(5+W)+W
4.5=2W
2.25=W
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L=W+5=2.25+5=7.75
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ANSWER: One solution is a 7.75cm x 2.25 cm rectangle.