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When i turn on my Samsung galaxy S5 it will not go past the T-Mobile boot screen.I tried to open through safe mode by pressing and holding the three buttons. First a warning page came, I pressed continue and a page shows OS is downloading, but I waited for 5 hours it didn't complete. I can't even turn the phone off without taking out the battery.
Welcome to Android Central! That's not Safe Mode -- that's Download Mode (aka Odin Mode). The "Downloading" message doesn't mean it's actively downloading -- only if you're connected to a PC via USB and have started downloading a firmware file.
To try booting into Safe Mode follow these steps: https://support.t-mobile.com/docs/DOC-28456. You can also try booting into Recovery and wiping the cache partition: https://support.t-mobile.com/docs/DOC-28028