[leatherneckpa]

Assume that a 37% by mass HCl stock solution will be used to prepare 500 g of a 5% aqueous HCl solution.

I calculated the molar mass of the HCl to be 36.46 g/mole.  A 37% solution would have 370 grams of HCl.  This indicates a concentration of 10.1M.

Next I calculated the concentration in a liter of 5% HCl.  A liter of 5% concentration would contain only 50 grams of HCl, or 1.37M.  Using M1v1 = M2v2, I wound up with needing 6.78x10-2 g of the stock solution diluted into 500 ml of water.  But I think I'm missing a few things here.

First of all, since it says “stock solution” that means it would be aqueous as well, right?  So then, do I need to calculate the mass of 1 l of this solution first?  How does one calculate the mass of 1 l of water?

And then, at the end, I need to convert the ml of of solution back into grams, right?

[Borek]

A liter of 5% concentration would contain only 50 grams of HCl

No - 1 kg of solution will contain 50 grams of HCl. You don't know solution density, so you can't say what is mass of 1L.

Are you sure you have to give answer as a voulme, not as a mass of solution? If so, you will need to check solution densities in density tables.