The fifth amendment does substantially more than protect you from having to answer "did you do it".
Scenario:
You are innocent of the crime you are accused of.
Prosecutor: Were you at the scene of the crime?
Accused: Yes.
This statement can be used against you to find you guilty.
Prosecutor: Did you have anything against the victim
Accused: Yes.
This statement can be used against you to find you guilty.
Prosecutor: Do you have a gun?
Accused: Yes.
This statement can be used against you to find you guilty.
Prosecutor: Were you having an affair with the victims wife?
Accused: Yes.
This statement can be used against you to find you guilty.
I could go on and on and on. We know from the outset of this scenario that the accused is not guilty but each and every one of his statements can be used against him in court to find him guilty despite his innocence.
This is why we have the fifth amendment.