Taking a look at FDOT GIS data from 05/22/21, it says FL-5 ends pretty much right where I currently have it on the site.
I found one of those FL-5 signs along US-1 that you were talking about
here. I think those are just contractor posting errors since FL-5 is suppose to be hidden under US-1 & US-17 in the state except for that segment in
West Palm Beach (FL-805 takes over under US-1 in this area) &
Jacksonville (recently signed after US-1 was properly moved to I-95's C/D lanes in that area after recent construction).
On a side note, I might have to tweak that Jacksonville one some per this
new signage I just found via StreetView from Jan '21.
Anyways, I think the West Palm Beach route doesn't need to be adjusted.