A 2 way flight from JFK(NY) to Bucharest(Romania) seems to be less than 1000 USD.
5000 $ easily buys you 3 weeks of wildlife shooting around here.
Country is part of the EU so it is pretty safe (safer than the UK, Belgium or Germany for example) and most people are fluent in English.
In May there is the bird migration and mating season in the Danube Delta so you got millions of birds descending from everywhere (pelicans, all manners of herons, wading birds, kingfishers, bee-eaters and so on, not to mention otters and wild hogs).
The toughest part is to get a guide for all of it, as I don't think there are local photographers organizing tours for foreigners... hmmm.
Depending on the season, you can go in the span of 24h from shooting brown bears, buffalo and deer to shooting flamingos or vultures.
Beer is cheap (at least compared to the rest of the EU) and wine is decent too
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