Been playing a 4 since the mid 70's, added a five two years ago.Been playing a 4 since the late 60's and now this new band I joined does 7-8 songs that would not cut it with a 4.
...
I've been learning a ton of tunes in the last three weeks, while at the same time trying to adjust to a 5.
...I'm also having trouble with left hand-right hand coordination, which means that sometimes I do not pluck the correct string. Othertimes, it's the other way around...I'll pluck the correct string but my fretting hand will be on the wrong string. ...
This may be part of your issue. Learning tunes and adjusting to the five at the same time, your brain is concentrating on too many things at the same time. You may want to spend some of your practice time just playing tunes you already know, without any changes, and use that to get the muscle memory to adjust to the five. Ignore that B string while doing this. This should help with that left-hand/right-hand coordination, but expect that to occasionally happen for a while.
Now, the following probably doesn't apply as much to your situation, since you need the five for your gigs, but I'm including it for completeness, and information for others.
I was lucky enough to not be learning new material, so I didn't have that distraction. I got my 5-string, practiced for a week, and played it in church the next Sunday. Yes, there were a few mismatched fret/pluck combinations, but not many, and I adjusted quickly. I also used the B string sparingly at first. And yes, even though I knew the songs well, it took some extra concentration.
Some advocate putting the 4-string aside and only playing the five for a while. I'd read enough threads on here where people commented about having trouble playing the four after a prolonged period of only playing the five, so I alternated, some weeks playing the 4, some the 5. This got me thinking of them as two different instruments.
I took a couple of months, but by then I was comfortable on both instruments, and was using the B string as just another string on THAT instrument.