BO last stitch when next step is to rejoin yarn

I need a bit of help figuring out what to do w/ my last BO stitch when the next step in my pattern has me rejoining yarn. Here’s what it says:

(with 23 sts on ndl) BO 9 sts, k4 (5sts on rt-hand ndl), BO remaining 9 sts on lft-hand ndl, ending up with 5 stitches.
I get that I’ll have 5 stitches left in the center of my work, but the next step is:

With RS facing, rejoin yarn to 5 sts on ndl. Cont in St st for 4"…

Do I cut my yarn when I BO my last stitch, and then add new yarn as if my skein was gone (for the rejoining to the 5 sts), or do I somehow have to keep my working yarn “working” after I bind off?

I appreciate any clarification/help/wisdom/etc !!

Yes, cut your yarn after you bind off the last of the stitches just like it was the end of a project. Then with the right side of the 5 stitches you have left facing up begin knitting with the same yarn ball you had been using.