Can I claim my 76 year old sister that lives with me now.

It depends.  You may be able to claim your sister as your qualifying relative. The following questions must be true:

• The individual can’t be claimed as a dependent by someone else. 
• The individual must be a U.S. citizen, resident alien, national, or a Canadian or Mexican resident. 
• If the individual is married, they can’t file a joint return with their spouse
• The individual must live with you all year.
• The individual  can’t have made more than $5,050 in income in 2024.
• You must provide more than half of their total support for the year.

 Please review the TurboTax Help article Who can I claim as my dependent?

Maybe.    Did she have less than $5050 of income not counting Social Security?   Did you pay for over half her support?

IRS interview to help determine who can be claimed:

https://www.irs.gov/help/ita/who-can-i-claim-as-a-dependent

If she is a "qualified relative dependent" you can get the $500 credit for other dependents, and possibly Head of Household filing status.

Qualifying relative

• They don't have to be related to you (despite the name).
• They aren't claimed as a dependent by someone else.
• They're a U.S. citizen, resident alien, national, or a Canadian or Mexican resident.
• They aren’t filing a joint return with their spouse.
• They lived with you the entire year (exceptions apply).
• They made less than $5050 in 2024 (not counting Social Security)
• You provided more than half of their financial support.

Am I Head of Household?

https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-filing-status/qualify-head-household-2021/L0NxUtVc2_US_en_US?uid=m5x19jkx

• What is a "qualifying person" for Head of Household?

If you qualify as Head of Household, when you enter your marital status (single or married filing separately) into MyInfo, and then enter your qualifying dependent, TurboTax will offer HOH as your filing status.