If you can not access the dashboard, you can perform WordPress manual update.
Incompatibility of old site with new PHP version is a common issue. Updating your site manually can help you to resolve it.
To make manual update / upgrade you need to access FTP / SSH or File manager.
The steps are described in WordPress documentation here and in extended steps here. This is usually helpful if you move old site to new env, and you can not access admin panel due to old WP incompatibility with newer PHP version.