Please clarify something. You state that the JPG files are small, at 3 to 5 mp. Normally mp refers to megaPixels, but many people confuse this with mb (megabytes), and these are not the same. So what is the output size of the JPG, 3 to 5mp or 3 to 5 mb? Where are you seeing this number?
Furthermore, with a 24mp RAW original, there is no problem at all getting 3 to 5 megabytes when you export. Why? Because exported JPGs use compression technology, the size of the file can be compressed without (much noticeable) loss of quality. So if you are getting 3 to 5 megabytes, there is nothing wrong here, and the files are probably fine. You should look at the exported file with your own eyes and see if the quality is what you expect.