Clearing Flag Bits By Writing 1
No, because then you could possibly clear other bits you didn't intend to by accident. It's a little hard to verbalize, but it is very easy to write a 0 simply by, well, writing a 0. You must deliberately choose to write a 1.
Since every position expects a 1 in order to clear it, write a 1 only to bit 5:

STATUS = _BV(TX_DS);