>I always thought the latitude and longitude values had a precision of five decimal places. But, Google Geocoding API returns values with a seven decimal precision. Is this the proper precision to use?

That obviously depends on the degree of accuracy you requre. One degreee of latitude is 69 miles (give or take a bit)
With longtitude then the level of accuracy for a given precision improves the farther North (or South) you are of the equator...