Database issue on upgrade to 2.5 on shared hosting
Have you checked craft/storage/runtime/logs to see if there's an error in there related to the update?

In case it is the database: you can disable the database backup during the update by changing https://craftcms.com/docs/config-settings#backupDbOnUpdate to false in general.php 

Remember to make a database backup every time you run an update when you change that setting!