Cannot start the application. Application data may be corrupted
According to the official PlayStation Knowledge Center, these issues can be resolved by rebuilding the database and/or reinstalling the PS4 system software. You can find instructions on how to perform these two steps below.
Before You Start
Before taking the necessary steps to fixing the CE-30002-5, CE-33177-1 and CE-35657-6, Sony suggests taking some precautionary measures.
First off, you should delete the failure notification. You can do so by going to the “Notifications” section (simply press up when you load the system menu to find it). After go to “Downloads” and then find the failure notification. Press the options button on the DualShock 4 to delete the message.
Furthermore, you should also back up the data stored on your HDD. To do so, enter the “Settings” section of the system menu and then select the “System” option. Afterwards, choose “Back Up and Restore” and then “Back Up PS4” in order to copy the data from the console’s hard disk drive on to a compatible external device. You can then return here to restore the backup data to the HDD after you are done with rebuilding the database and/or reinstalling the PS4 system software.
Step 1: Rebuilding the Database
After you are done with the above preparations, turn off your PlayStation 4. Now press and hold the power button of the system for seven seconds (you can let go after hearing the second beeping noise). Follow the instructions on screen to connect the DualShock 4 by using an USB cable to the PS4. This will lead you to Safe Mode.
From there, scroll down to the fifth option, which is Rebuild Database. This option will enable the system to scan the HDD and create a new database, hopefully solving the CE-30002-5, CE-33177-1 and CE-35657-6 errors in the process.
Step 2: Reinstall System Software
If you are still running into the same problems after rebuilding the database, Sony suggests re-installing the system software. Doing so will delete all the data from the HDD, including the firmware. If you already created a back up on an external device like we mentioned above, this shouldn’t be too troublesome (you may have to download the latest PS4 firmware and put it on the same USB device, however).
To reinstall the system software of the PlayStation 4, you can select the seventh option from the aforementioned Safe Mode. Afterwards, you can restore the backup data from the USB device.
Hopefully, by rebuilding the database and/or reinstalling the system software, the CE-30002-5, CE-33177-1 and CE-35657-6 error codes will no longer be a problem.