How many trees can I put and they produce in this garden area? The garden is 10 ft x 5 ft and 18 inches deep. Please advise  

Myself, I would only put one tree in that size area.

One, if you want to maximize productivity. Two, if you want to maximize number of varieties.

two would work nicely.

You could get 3 in there but....

I did the bulk of my in ground fig planting winter of 2014-2015 (last year).  To get as many trees as possible I planted most on 7 feet centers.  I was able to squeeze 60 trees in ground, but very few in full sun.

My faster growers Bourjasotte Noire, Sultane, MBVS, RDB now in their second season are already growing together, making walking around them more difficult and I HAVE to pinch them.  

If I was doing it over I would give 10 feet minimum.  They will still grow together, but it would keep them from shading out other varieties. I knew I would have to prune them, but I didn't know it was going to be quite so soon.  Our season is so long and hot they grow like mad here.

Personally, I wouldn't plant more than 2 at most (one would be best IMHO), but you will be busy pruning, which may or not be a bad thing.  Looks like a sunny spot so that will definitely help.

I was thinking the same thing like Alan. Also some varieties are very slow growers some are super fast growers. Some grow like shrubs while others grow straight up.
The following is a "temporary" arrangement of some of my trees. The roots are confined in a five gallon container one foot apart and the trees are not allowed to really grow. The crop if any will be minimal 10 to 20 figs per tree per year as I did not try to put my feeding in overdrive, but low air circulation will also affect results negatively. The trees you see are over three year old.
Having my trees in containers on a temporary basis gives me greater flexibility when it's time to up pot or move them to a permanent location. If these were in ground that tight, I might lose the ability to maneuver or control them properly and would never plant them that close.

People see a lot of photo's of itty bitty fig trees making figs and the idea of them getting big just doesn't sink in until they start to do that very thing.

 

It depends on how you plan to grow them.
Will you be digging them up each year and root and balance pruning them? 
If so you could get 6 figs for a few years. 
Then you would need to reduce the number as they get bigger and end up with 2/3 fig trees. 
I was told Figs prefer to be grown in pairs. 
Two would fit nicely in the long term with annual pruning.

One

Wow, so much to think about, but believe me some of these trees are going in that garden.

Hey Alan your comments that "Thickness is my first priority because of the strong winds and the cold weather. In time I will decide how tall I will let them grow. I never grow mine like a tree any more because of the wind catching it that way. I also think that growing like a tree it causes more shade. I grow mine like a bush and try to thicken them up like a tree. Cold damage gave me the idea. Then I found out that some people in France grow them like that, helps with the wind, it supposedly makes for higher/better production as well. I am hoping for 6 to 8 inch thick fig trees. So far they are thickening up very nicely."  Can you tell us or show us more about this?  I think this would be the way to go for me, but I do not know how to do it?  Or point me to a post that explains it further.  The learning goes on....Thank you, Jodi

I have 73 in ground figs, I have always let them grow in bush form but
I try to only keep 3 main tree trunks on each tree.
It lets those 3 stalks get all the nutrients. Works well.

Doug