My son is a 21 yo college student. I paid more than half of his living expenses. He earned 5,050 in an internship, and TT says that he does not qualify as my dependent

 Try this: revisit the entry in the "My Info, Your household" section. Make sure all the interview screens have been completed accurately: 

• Navigate to My Info, Your household, select your son
• Choose "My child", continue and be sure his name, date of birth and proper citizenship is complete. 
• Continue, and answer the question about living arrangements and parents. 
• Continue, and answer any less common situations. Here, make sure "was a full-time student in 2024" is checked.
• Lastly, enter the child's SSN and be sure that "Not valid for employment is printed..." is NOT checked. 

Also, he will not qualify for the child tax credit, but he may qualify for the $500 credit for other dependents, if he is a dependent.

Here is some more detailed information: Rules for Claiming Dependents on Taxes

There are two types of dependents, "Qualifying Children"(QC) and Other ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test.

A child of a taxpayer can still be a “Qualifying Child” (QC) dependent, regardless of his/her income, if:

1. He is under age 19, or under 24 if a full time student for at least 5 months of the year, or is totally & permanently disabled
2. He did not provide more than 1/2 his own support. Scholarships are excluded from the support calculation
3. He lived with the parent (including temporary absences such as away at school) for more than half the year

So, it doesn't matter how much he earned. What matters is how much he spent on support. Money he put into savings does not count as support he spent on himself.

So, if he doesn't meet the rules for a QC, we then look at his income. If it is more than $5050, he can not be a Qualifying Relative either. 

See full dependent rules at: https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Return/INF12139.html