No, planting another variety won't help. Fig pollination is a bit more complicated than most fruit. In areas outside of southern California you should plant only figs that can produce fruit parthenocarpically. For the most part this isn't something to worry about as few nurseries sell the type that requires pollination. But it could be a problem if you plant seed from a dried fig, or if you dig up a seedling tree you find while on vacation in Southern California.

If you know it's been there for 5 years and it still makes no attempt at producing figs -- then you should simple replace it with a known variety for your area.

But look closely at what you currently have before putting another one in at the same spot. Does it get full sun for at least 6 hours/day? Is it frozen back each winter? Many varieties won't produce the following year after being frozen back. Does it make fruit that never matures, but drops off well before winter comes? If so, it may really need pollination, and you'd need to replace it with a different tree.

Here is a link that might be useful: Weird Sex Life of the Fig

I snapped some pictures that may help to identify.
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Based upon these two pictures, I think there might be TWO figs here and not just one.

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And this might be promising:

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Perhaps this fig is just a victim of an over zealous church-lady with pruning shears?

It is a bit hard to tell from your pictures, but it would appear as though:

Tree #1 may not be an edible fig tree.
Tree #2 is not an edible fig tree.

Which is #1 and #2? the one with the long skinny finger type leaves or the fat finger leaves?

Either way when nobody is looking I'll replace themn with bearing varieties....

if I plant a bearing fig in the spring when these are both pruned back.. I can selectively remove the non bearings by progressive pruning and allowing the bearing variety to flourish.. by the end of 2 bseason we'll have a healthy, bearing, bush and no more non-bearing bushes ;-)

Looks like 1 is definitely a mulberry to me. If its non-bearing, then I would guess you have a male.

Sandsquid, what zone do you live within?

~Chills

7a.... Memphis, TN