Calculating distance between previous and current addresses for large file

Hoping to get help with this: I'm a fairly new QGIS user and trying to solve the following problem: Let's say I have a large dataset (5000 + records) of customer addresses, previous and current, and I want to calculate the distance moved for each customer. Ideally this would be via roads, not as the crow flies, but this is national-level data and I don't yet have any shapefiles for roads covering the whole country (US). I don't have the file yet, but I believe it will have lat/long.

A) is there any way to do this without locating/downloading a national street file? B) How would I go about solving the problem either way?

Thanks!