The answer to your question in the heading is... yes.
The Free 5.0 is not just neutral but technically a "minimalist" shoe - allbeit a fairly cushioned version of one.
Given your bursitis issues, it is one of the few shoes I can think of that has the super soft heel counter you need - but remember it has a lot less structure than most standard neutral road shoes so will make your feet have to work harder and support themsleves (as avit points out above) - and why they will feel sore.
Let them recover and keep going - may start back with some runs of only 1 mile this time while your body adapts - and build up to 3.