I claim two dependents and file married filing separately. I have only had 5 dollars of federal tax taken out. I’m a little confused about why I’m not being taxed.

The W-4 you gave to your employer does not dictate how you will have to file your tax return.   When it is time to file your return you can file a joint return, married filing separately or perhaps as Head of Household, depending on your circumstances.  You should be mindful, however, of how you actually intend to file, because your standard deduction and your child-related credits are affected by the filing status you use when you prepare your tax return.

One thing needs to be mentioned--if you are really filing MFS you will not be eligible for earned income credit.   If you are eligible to file as HOH because you live apart from your spouse and have the children then you may be able to get earned income credit.   Filing MFS disqualifies you for EIC.   You can get the child tax credit if you are filing HOH or MFS if the kids are under the age of 17.

If you are married and live with your spouse then filing a joint return is almost always best when you have children, because you lose child-related credits if you file MFS.  You lose EIC and the childcare credit, and/or you lose education credit if you have a college student.

Am I Head of Household?

https://ttlc.intuit.com/questions/1894553-do-i-qualify-for-head-of-household

https://ttlc.intuit.com/questions/2900097-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.

If you were legally married at the end of 2023 your filing choices are married filing jointly or married filing separately.

Married Filing Jointly is usually better, even if one spouse had little or no income. When you file a joint return, you and your spouse will get the married filing jointly standard deduction of $27,700 (+$1500 for each spouse 65 or older)  You are eligible for more credits including education credits, earned income credit, child and dependent care credit, and a larger income limit to receive the child tax credit. 

If you choose to file married filing separately, both spouses have to file the same way—either you both itemize or you both use standard deduction. Your tax rate will be higher than on a joint return.

 Some of the special rules for filing separately include: you cannot get earned income credit, education credits, adoption credits, or deductions for student loan interest. A higher percent of your Social Security benefits may be taxable. Your limit for SALT (state and local taxes and sales tax) will be only $5000 per spouse. In many cases you will not be able to take the child and dependent care credit. The amount you can contribute to a retirement account will be affected. If you live in a community property state, you will be required to provide additional information regarding your spouse’s income. ( Community property states:  AZ, CA, ID, LA, NV, NM, TX, WA, WI)

 If  you are using online TurboTax to prepare your returns, you will need to prepare two separate returns and pay twice since with online, you get one return per fee.

https://ttlc.intuit.com/questions/1894449-married-filing-jointly-vs-married-filing-separately

https://ttlc.intuit.com/questions/1901162-married-filing-separately-in-community-property-states

https://ttlc.intuit.com/questions/1894449-is-it-better-for-a-married-couple-to-file-jointly-or-separately