Spiral balance for single hung tilt sash. 5/8" diameter tube 22-3/8" long.

Thank you for reaching out to us. I would recommend the S600-22 with the blue tip. However, I'm afraid the window might be too old to use the 75-069 jamb spreader, as there's a risk of damaging the brittle vinyl. 

Take a look at the video below on the cut-out method, which is our go-to suggestion for removing the old pivot shoe. 

For us to ID the pivot shoe, we will need to see it removed from the window sash, along with the written-out thickness and width.