"The sacks weigh 5.5lbs, 6.5lbs, 7lbs, 4.5lbs and 3.5lbs respectively. Considered together, each of the sacks is weighed twice, except '3', which is weighed three times. Add all the totals together, and subtract twice the weight of '1' and '2' combined, and also twice the weight of '4' and '5' combined, and you'll get 21, which is three times the weight of '3'. From there, you can substitute easily to find the values."
Notes
Dedopulos, T., The Medieval Puzzle Collection (London, Cartlon Books Limited: 2014) p. 91
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