Is it possible if I mix Laravel 5.7 with this vue template : https://github.com/DivanteLtd/vue-storefront ?
Vue Storefront is not a template. It's a eCommerce framework with it's own API and database (see this architecture diagram).
If your question is about using Vue Storefront with your custom Laravel backend then it's doable. VS is meant to be backend agnostic which means it can work with any backend if you provide appropiate connector. https://github.com/DivanteLtd/vue-storefront-integration-boilerplate - here you can find integration boilerplate. There are few more resources on this topic in VS readme.
Also in case of any problems feel free to ask on community slack https://join.slack.com/t/vuestorefront/shared_invite/enQtMzA4MTM2NTE5NjM2LTI1M2RmOWIyOTk0MzFlMDU3YzJlYzcyYzNiNjUyZWJiMTZjZjc3MjRlYmE5ZWQ1YWRhNTQyM2ZjN2ZkMzZlNTg