it's called growling where you growl with your throat while playing the note. there are many videos on YT about how to do it.
on top of it, Dexter rolls his fingers down the scale to make that descending effect. he does it first without the growl then again while growling.

 

Yes, That’s the r-r-r-r-r-olling R type of growl versus the hum type achieved by audibly humming a pitch while playing.

 

Sounds like a flutter tongue.

 

Which is essentially the same as the rolling style "growl" effect.

 

here is a video explaining it, starts at 2:18

 

Well, flutter tongue is making the rolled "r" sound (think of the Spanish letter rr) while playing. Growling is vocalising while playing - whether an actual pitched hum or just a general "growl" type vocalization.

Flutter tonguing and growling can sound similar, but flutter tonguing is much more raucous, also less controllable. Growling can range from just the slightest roughening of the tone to a very heavy effect.

The actual physical techniques are quite different; the names reflect the technique. Doesn't have anything to do with classical or jazz.

I listened to the referenced song and at 5:13 I clearly hear a brief, very well controlled - flutter tongue - NOT a growl.

Listen to Arnett Cobb below, the chorus starting at around 2:10 is all growled. One of his signature techniques. Note how it's not individual flutters, it's an overall thickening of the sound.

 

That is very clearly a flutter tongue, not a growl. It's important to use the right terminology sometimes.

 

Flutter tongue with growl, into a fall. Kind of odd to do that in a ballad like that.