I have a Texas Everbearing that died to the ground. It has already sent up 5 strong thick shoots about 8-10 inches tall. These will form the base of the new bush. But this morning I noticed several new shoots coming up from the roots as well.

So here is my question. Should I pinch all shoots besides the 5 large ones so that all the root's stored energy goes into them? Or should I let everything grow up and just prune next winter. 

BtW, my goal is max fruit production this year.

GeneDaniels,
Limit the number of branches to the 5.
The tree will put more energy into vegetative growth instead of fig production if the excess multiple branches are not pruned.
Good Luck.

Here is what it looks like right now:

 
Those little trunks are almost as big around as my fat fingers, much thicker than the shoots I see on my other figs.

Great question.  I have a tree that's doing the same thing.  Thanks for the advice, Pete.

Hi GeneDaniels,
Do you want to propagate the tree ?
If yes, then keep some additional shoots and airlayer them as soon as they are three inches of height.
If no, then they are just "garbage" and as such you should take them out as soon as you spot them.
Those shoots being the closer to the roots they will drain a lot of energy for nothing.
For the five shoots you are keeping, try spreading them so that they don't shade each other. That will help grow quicker and as always, fertilizer, fertilizer ... and proper watering .
Today here it is raining, so my watering tasks are already completed :).