1972 Schwinn 10 speed missing chain need to know how many links
There are two different techniques used to size a chain for a multi-speed, derailleur bike.  The specific one to use is based on the number of teeth the largest cog of the freewheel has. One method is used if the large cog has 27 teeth or less, the other method when the large, rear cog has more than 27 teeth.  On a bike like you describe, with a five speed freewheel, the largest cog will have 28 teeth or less.

First method for bicycle with a rear cog having >27 teeth: WITHOUT going through the rear derailleur, wrap your new chain around the large front chainwheel and back and around the large rear cog bringing the two ends of the chain together.  Essentially you've now wrapped the chain around the large-large combo, eliminating the rear derailleur. The chain ends will come together and you should note an overlap of a few links.  The properly sized chain will be +2 links (that would be 1 inner link and 1 outer ink of the chain) past the point where the slackless, wrapped chain comes together.

The second method should be used if you're sizing the chain when the large rear cog's teeth number 27 or less.  In this instance, you'll wrap the chain around the larger chainwheel and around the SMALL rear cog.  You must thread the chain through both derailleurs so it's necessary to have them (and therefore the shifters) in the correct position (large front: the inner shift cable will be under tension, and small rear, where the rear's inner cable is under little to no tension).  With the chain wrapped as described, you will bring the ends of the chain together (note that you'll be pulling one side of the chain against the spring tension of the rear derailleur which will create movement of the derailleur's cage/pulley wheels).  Continue to bring the ends together and overlap until the the rear derailleur's cage is straight up and down.  More properly stated, the correct chain length is achieved when a line drawn through the center of the upper guide pulley wheel and lower pulley wheel is 90 degrees to horizontal.  Please refer to the diagram on page 28 of the following link:

Shimano General Operations.
Page 28 deals with chain sizing on road bicycles having two front chainwheels and multiple rear cogs.  Keep in mind that your connecting link is an outter link and that you'll eventually join your sized chain where each end is an inner link.