Earned income credit is based on two calculations. First, your income earned from working, and second, your total income. With $5000 of earned income, your maximum EIC is around $2000. $5000 would be the correct EIC if you had $25,000 in earned income, but your $20,000 of unemployment compensation does not count as earned income. My guess is you filled out the worksheet incorrectly and TurboTax is correct.
And don't forget about the 10,200 unemployment exclusion. That will reduce your AGI Adjusted Gross Income. Did you file early before the exclusion?
Also did you see the question that you can use your 2019 income to calculate the EIC? The special lookback rule will allow lower income individuals to use their earned income from 2019 to determine their Earned Income Tax Credit and the refundable portion of the Child Tax Credit in 2020, since their lower 2020 income could reduce the amount they are eligible for.
You may use your 2019 income for the Child Tax Credit if your 2019 earned income was morethan your 2020 earned income. If your 2020 income was more than your 2019 income then you cannot use the 2019 income.
You can look back and use your 2019 income for the EIC credit instead of 2020. How to use the Lookback provision
I did a test return using the info you gave ... and if you used Single or HOH filing status the amount is the same either way ... before and after the unemployment exclusion the refund is the same $3253. Now if you want to recompute using the LOOK BACK option that uses the 2019 AGI then feel free to try.