I don't think 5,000 years is long enough. And how won't viruses hurt them? Their pathogens would affect us adversely and vice versa. They wouldn't be invasive species per se as the environment is still catered to their existence at this point in time.
A dinosaur? Sure, not so much. A recent extinction from an age we're still actually in? I see no issue there. You also probably don't understand just how massive Alaska actually is. Nothing you could do could significantly hinder anything, and the life web covers pretty much the entirety of the state.
The main issue of course would be that you would need to bring back their original diet, if it has also gone extinct.