Yes, it’s possible however it is illegal and not easy to go out Shenzhen area without a Chinese Tourist Visa, here’s why.
If you are planning to go out of Shenzhen, you might unable to board a plane, train and public bus since they require a passport for identification. And if they found out that you are going out of Shenzhen using a 5-day tourist visa on arrival, they might report you to a local police for trying to breach your visa conditions and eventually have you deported back to your country or to Hong Kong in most cases.
If you really want to breach your visa, hire a private car to take you out of Shenzhen but again, in China, things are limited without an identification which is your passport and they will always have a chance to check your visa.
It is recommended to get a Chinese Visa first in your country and it is easier for people who have been issued a visa before so it’s better to just apply for it.
Eligible countries can also apply for a Chinese Tourist Visa in Hong Kong but it might take longer since they process a thousand of applicants every day.
You may also ask an accredited agency to get you to mainland China and let them apply for a tourist visa for you.