Does Shenzhen have social security for five consecutive years?

You can't. Non-deep households who have paid social security 10 years in Shenzhen, reached the statutory retirement age and reached the prescribed minimum payment period 15 years, can choose to go through retirement procedures in Shenzhen or move back to the social security bureau where their household registration is located. Where you go through the retirement formalities, you can enjoy retirement benefits in that area. Non-deep households who have paid social security in Shenzhen for less than 10 years, reached the statutory retirement age and reached the prescribed minimum payment period of 15 years, can only move back to the social security bureau where they are registered to go through retirement procedures and enjoy retirement benefits at the place where they are registered.

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