Barnards Star, Lalande 21185, then Alpha Centauri, then Proxima Centauri, then Ross 248, then Gliese 445 makes 6. There are 6 if you count Proxima Centauri and

Barnards Star, Lalande 21185, then Alpha Centauri, then Proxima Centauri, then Ross 248, then Gliese 445 makes 6. There are 6 if you count Proxima Centauri and Alpha Centauri separately; 7 if you count both stars in the Alpha Centauri pair separately, and 5 if you count Alpha and Proxima Centauri separately. Alpha Centauri is the binary system of Alpha Centauri A and Alpha Centauri B, which are separated by about 10-30 AU. It's very, very close in terms of interstellar distances to Proxima Centauri, which is a red dwarf that orbits Alpha Centauri A and B at a distance of 13000 AU, or 0.2 LY - a remote enough orbit that it makes sense to keep track of whether it's on the near side or far side of the triple-star system.