MidwayUSA.com provides a shipping weight of 7.65 pounds for one box of 1000 rounds of Winchester M-22 ammunition, so five boxes of 1000 rounds would weigh 38.25 pounds. Shipping weights may vary due to packing differences between manufacturers and their distributors.
Typically, .22 long rifle ammunition is shipped in a wide range of box sizes with each round inserted into a styrofoam or plastic pack. It is also shipped loose in containers such as boxes, cans or buckets. MidwayUSA provides a shipping weight of 3.84 pounds for SK Mag 22 LR ammunition, sold in a can of 500; 5000 rounds of this ammunition would weigh 38.40 pounds.