Name sectors after bright stars
I'm an astronomer and therefore utterly awful at naming things, but I'll vote in favor of centering each sector around one bright star -- in particular, an O or B star -- and use whatever name people on the street call that star. In our local stellar neighborhood, these luminous stars have a combined number density of roughly $n\sim3.2\times10^{-5}$ per cubic parsec. The mean separation is then $d\approx n^{-1/3}\approx100$ light-years, so any point in space should be within about 50 light-years of an O or B star.
Now, this is larger than the 5 light-years you asked for, but bear in mind that all kinds of stars in our neck of the woods put together have an average number density of $\sim$0.1 stars per cubic parsec, meaning that the typical star is about 7 light-years away from its nearest neighbor. In other words, if we stick with your sizing scheme, the vast majority of sectors will have no more than 1-2 star systems within each one at the most, which seems like too fine-grained a measuring system. I'd argue a 100-light-year separation is better for practical purposes.
Some advantages:
- There are O and B stars throughout the galaxy, so wherever you go, you'll have new reference points.
- O and B stars are easy to find and locate and will likely be among the best-studied natural landmarks (spacemarks?) available.
- Using this coarser system means you can use words, like Nosajimiki suggested, to name sectors, without running out of easy-to-pronounce combinations any time soon.
Some disadvantages:
- These stars will die after a couple tens of millions of years at the latest; on the other hand, more will spring up in their places.
- They do tend to be clustered together and sometimes in binaries, so the separation I quoted above is a slight underestimate.