It really is a beautiful sound. I suspect he used his Oberheim 4 voice for this, if memory serves at the time of the Wichita Falls record he had that Oberheim and a Prophet 5, so one of those two I think.
There are a couple of ways to make string patches, trying to get one to sound exactly like this is probably quite hard, but getting one to sound almost like it should be ok.
There are lots of tutorials out there on youtube which go into much more depth, but for starters I would suggest getting two oscillators involved, one a square wave with some subtle pulse width modulation going on, and one a sawtooth maybe slightly detuned.
Then set the attack and release fairly slow on the amp, also have a slow attack on the filter envelope (but not as slow as on the amp attack). You can adjust the attack / release speeds to taste, as well as the envelope amounts
By the sounds of this patch I would also set the cutoff on the filter to not too high. Remember also the cutoff affects the filter envelope so bear that in mind when tweaking. I would only suggest a touch of resonance (if any).
Lastly for now try adding a bit of chorus too
This should put you in the right ballpark at least. Btw I don’t have a Take 5 but I think all the above features are available on it.
There are other ways to create string patches too, eg two detuned sawtooths, two pulse width squares etc. Try giving that a go too if the above doesn’t work!
Worth mentioning lastly that don’t lose heart if you can’t recreate it exactly - the recording uses a different synth to you, plus it has been wonderfully produced and eq’d too, and may well be going through some magic outboard gear! Though maybe finding a live version to try to match against could take some of that out of the equation.
Good luck!