37/100 x mass of 37% HCl =0.051kg thus mass of solution=0.139kg
I get 0.138 kg, otherwise your method is fine.
My final volumes are 116 mL of 37% HCl and 882 mL of water for 1 L of 5% HCl(aq)
I'm not sure about your method, try it and see what you get.