Hi there, Eric.
Thanks for reaching out to us. The difference between these parts is the coil weight. The S165-4 is a 4-pound spring, while the S165-5 is a 5-pound spring. To determine the proper coil weights needed for your sash, divide the sash weight by the total number of springs in the window. I'd be happy to confirm the S165 are what you need but I would have to see photos of your pivot shoe.
This is a huge help, thank you! You have our 15-199 pivot shoe which uses the 1/2" wide Series 160 and 3/8" wide Series 165. You'll have to measure the width of the coil spring band to see which Series is the best match.
I also recommend checking the band of the spring for a weight code. If there aren't any or are too faded to make out, you will have to divide the window sash weight by the total number of springs in the window to determine the appropriate coil spring weights.