If 12.5% of the trip has been completed when there are 5 hours and 50 minutes left in the flight, this means that 5 hours and 50 minutes = 87.5% of the trip. Converting this into minutes, we know that 87.5% of the trip is equal to 350 minutes.

We want to know what the clock will read when the trip is 50% complete. This means that the clock will read the amount of time left in the trip, which is also 50%. In other words, we want to find how much time 50% of the trip is equal to.

Let's set up a cross-multiplication equation using what we know.

$$\frac{350\ \min}{87.5\%}=\frac{x}{50\%}$$

87.5x = 17500

x = 200 min

Converting back into hours and minutes gives us 3 hours and 20 minutes, or 3:20, which is answer choice E.