After working for five years, the company has not signed a labor contract for various reasons, and the pension insurance for these five years has not been paid. What should I do?

You can apply for resignation on the grounds of not paying social insurance, apply for arbitration to pay economic compensation, and ask them to pay social insurance for you.

The company has no right to detain your money and several valid certificates, which is illegal. You can also apply for a refund. In this case, you can ask the company to sign a labor contract with you without fixing solution.

I suggest you apply for arbitration, and you can also apply for economic compensation without signing a labor contract.

Apply for arbitration to the labor bureau where your unit is registered.

Pay attention to keeping relevant evidence.

Further reading: How to buy insurance, which is good, and teach you how to avoid these "pits" of insurance.