What kind of programmer? Software engineer, game developer, web developer, mobile developer, data analyst/engineer/scientist, machine learning engineer, QA or test developer, DevOps specialist, database administrator, cybersecurity engineer, system administrator?

Of course it's possible to earn 5k as a fresh grad. But the fact that you used programmer as a gauge in your question (extremely vague) means you are probably not the one going to get paid 5k imo.