Could you please make sure that Lightroom is updated to the recent version, Lightroom 5.7.1
Also what are the export settings of Lightroom ?
Are you not able to export any image or is it specific to a few ?
My version indicates that it is indeed LR 5.7.1
Export to - Hard drive
Location - same folder as original
File renaming - no change
File settings - JPEG / sRGB
Image size - 300 ppi
Sharpening - off
Metadata - all metadata
Post processing - do nothing
Occasionally one image will export but only about one a day.
How many images are you exporting from Lightroom ?
Also could you please try to create a Test Catalog and then try to export the images from the new catalog.
My export box has started working again on its own, I have no clue what the problem was but am glad it is working once again.