The next size is #8, used for Big Stitch quilting and for sashiko.
Then there's #12, a finer perle that I use for both embroidery and some hand quilting. Quiltmakers who love wool use all three weights (5, 8, and 12) when doing buttonhole stitch or other applique techniques in wool.
Lastly #16 is the finest of the perles, loved by knitting fanatics and tatters who work with super-delicate thread. A few hand quilters have also discovered that #16 also works for quilting. Presencia is the only company to make the complete range of sizes of perle cotton.
You can leaf through the Presencia catalog online here http://www.presenciaamerica.com/files/Presencia_America_catalog.pdf but you won't find Presencia thread in chain stores. Look for Presencia perles being sold by independent retailers and needlework specialists.