How can I prepare 500g of a 5% aqueous HCl solution,given a 37% by mass HCl stock solution?

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In a stock solution 37% HCl and 63 % water.

So astock solution of 100 gm contains 37 gm of HCl.

Therefore a 5% of 500 gm solution should contain 5% of 500 = 25gm HCl.

25 gm of HCl is there in (25/37)100 gm of stock solution . Or

25 gm of HCl is there in 67.56756757 gm of stock solution.

So in a 500 gm of 5% solution, There is 25 25 gm of HCl implies it is a stock solution of 67.56756757 gm and 500 - 67.56756757 gm = 432.4324324 gm of water.

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