Just to be clear, I don't think you can actually make a 5M solution of copper sulfate, but I'll ignore solubility for this answer.
When you make a solution of a given concentration from a solid you generally dissolve the solute (your copper sulfate pentahydrate) in a relatively small amount of water and then dilute it to the final volume. Here, you would dissolve your 249g (1 mole) of copper sulfate pentahydrate in sufficient water to dissolve it but less than 200mL total, then carefully add enough water to reach a solution volume of 200mL, yielding a 5M solution.
The water of hydration would indeed become part of the solution. If instead you began this process with anhydrous copper sulfate and used 1 mole of that (159.61g) then you would dissolve it in enough water to make the solution but less than 200mL total then carefully add enough to reach your final solution volume and concentration, 200mL at 5M.
The difference here would be that you would have to add 90g of additional water to prepare a solution from the anhydrous compound as compared to the pentahydrate.
If you prepare a solution by adding a fixed mass of solute to a fixed volume of water, you are never going to make the desired concentration and volume.