Will I qualify for Virginia unemployment?

I was recently fired from a job I had for five years. I had no warnings, no write ups, but they said they had been auditing my activity for five months and that I had too much idle time and was reporting things incorrectly. Before this, I had suspected that a couple of managers were not happy with me because they were being snappish, so I confronted them and asked them if I had done something wrong, and they said no, I was fine and it was other things. This company has a habit of firing people out of the blue, with no warning, so I was paranoid about it. Fast forward a month, and I'm fired, and they knew the whole time.

Besides the fact that I fully disagree with what they were claiming, since there was no warning, and I even inquired about my job performance, can they still prevent me from getting unemployment?