I have used LightRoom for years and just started having this issue. I select all of my raw images and "Open with" LightRoom 5. I can view all of the images that I want to import. It then imports only some. There are times it will import some and then freezes up in Import mode. I have even converted images to dng and found it to do the same thing. As a professional photographer this is frustrating!
If you mean "Open With" in your operating system, I am surprised that you get any images to import this way. As far as I know, Adobe has (tried to) disable this as a method of importing photos, and so I doubt you will find any help here in this forum on this matter, as this is not a function of Lightroom (although you used to be able to do it in earlier versions).
It has always worked for me. Even if I import files from Lightroom I still have this issue.
What error messages do you get when you use FIle->Import?
What is your operating system?
What version of Lightroom 5?
Are the photos you are trying to import on a camera card, or on a hard disk?