Why does 8085 microprocessor has 8 bit flag register when it has only 5 flags?

The 8085 microprocessor has an 8-bit flag register, even though it only has 5 flags, because all of the registers in the 8085 are 8-bit or 16-bit. In fact, the flags register is considered to be part of the accumulator, as one "register pair", for purposes of stack push/pop and interrupt call/return.

Be warned, however, that you should not attempt to change the state of bits stored on the stack and then pop'ing them into AF, because some of the three "unused" bits might be undocumented but actually used, or their meaning might change between different versions of the chip.