Roth-IRA Contribution

This might not be the best place to ask but I'll give it a shot. So basically I was wondering how much I am able to contribute to my Roth IRA without penalty. In 2020 my income was 5k. And I lost my job due to the pandemic and started dental school later in 2020, so currently I am unemployed. I was wanting to contribute to my 2020 Roth Ira before the 2020 cutoff and am wondering if I could contribute the full 6k yearly limit or only the 5k that is on my income. I'm also assuming that now in 2021 since I am unemployed and a fulltime student if I made any contributions to my 2021 Roth IRA I would get penalized.

TLDR; With my 5k income in 2020 can I contribute the full 6k yearly limit?

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Thank you to any advice you might have to offer!