Hey there, klija1950.
I wouldn't say that a healthy HDD would be causing those issues with games like TF2 and CS: GO, even if it's a 5400RPM drive. Basically the storage does not play a huge role once the game has been loaded.
However, if you think that there might be something wrong with your HDD, I'd recommend that you backup your important data, just to be on the safe side. After that go ahead and try the drive with a different SATA port and cables, to exclude the possibility of a faulty connection.
You should also download DLG (Data Lifeguard) and run both tests (Quick and Extended), to see if there's anything out of the ordinary. Here's how to do that:
How to test a drive for problems using Data Lifeguard Diagnostics for...