I realize I'm 5 years late but here's the solution:
I will be using "sqrt" in place of a square root sign (FYI)
The bottom triangle is a 30-60-90 triangle. This means that the side shared between the two triangles will be xsqrt(3) in regards to that lower triangle. (look up 30-60-90 triangle and memorize its proportions)
Now find the expression on the top triangle in regards to that same SHARED side. It will be sin(θ)=x/5. Multiply both sides by 5 to get: 5sin(θ)=x
Now we are expressing the same SHARED side where the two triangles meet with two different expressions that we can set equal to one another to get 5sin(θ)=xsqrt3
Divide both sides by sqrt3 to get x=5sin(θ)/sqrt3 now just rationalize to get x=5sqrt3 sin(θ)/3
This equals the missing side, x. Some may think thats the shared side but remember the proportions of the 30-60-90 triangle where opposite 30 is x, and opposite 60 (the side that is shared) is xsqrt3.
