Ultrasonic sensors face to face
Yes, it is possible to measure distance by timing propagation of sound.  The accuracy depends on how well you know the speed of sound, and how well you can measure the delay.

I'd expect that both sensors measure half of the distance this way.

This makes no sense at all.  First, the sensors are measuring sound level.  The overall system might use that to measure distance, but the sensors don't.  Second, I can't even guess how you think that the data from one sensor somehow tells you half the distance.

Let's take a look at timing.  Sound in typical air takes about 3 ms to propagate 1 m.  Your distance is 5-10 meters, so the delay from transmitter to receiver will be in the 15-30 ms range.  That's a "long" time for a microcontroller, which can easily measure that to high precision and accuracy.  A counter running at 1 MHz, for example, would get to 30,000 counts in your maximum time of 30 ms.

However, the real problem with accuracy is detecting when exactly a sound pulse is received.  Common ultrasonic emitters and sensors work at around 40 kHz.  That means the wavelength is about 8.3 mm.  It will be difficult to get much more accurate than that.