Power button functioning as volume up key I just want to know if it is a software or hardware problem?
What I think is If the key is working fine and performing different function, It must be software problem but I am afraid that I I tried anything I might not able to turn it back on again. neither I would be able to enter recovery mode
TL;DR It's most likely a software problem

Check for incorrect ROMs or button remapping root mods

It sounds like a software problem. Do you have custom ROM installed? Is your phone rooted? With either of those two cases, you likely have some software setting that overrode the button mapping of the hardware keys. Perhaps you installed a ROM that was designed for a slightly different version of your phone.

In any case, the functionality of the power button cannot be rewritten at the hardware level. I feel confident in telling you that you should be able to turn off your phone, and the power button will act as a power button to turn the phone back on. That's built in to the hardware, and only after the ROM boots should it be able to act as a different button.

If you want to test it safely, I suggest pressing and holding the power button for 15 seconds, (don't use the Android power menu to turn the phone off). Almost all Android phones will force shut down if you hold the power button down for long enough, including the Zenfone 5.

In the case that it's only a software problem, your volume will turn up (as if you are holding the volume up button), but then the lower-level hardware will still shut the phone down after you continue to hold the button down. Since the phone detected the power button and shut down, you can be confident that it will detect the power button to turn back on.

If holding the power button down for 15 seconds doesn't power off the phone:

If, on the other hand, the phone does not turn off after holding the power button down, and it only acts like a volume button, then you may have some bizarre hardware problem. 

Perhaps the phone got wet and the contacts got shorted. The Asus Zenfone 5 has the power button and volume buttons next to each other (are you sure you are actually pressing the power button and not the volume button?). In this case, if holding the power button down for 15 seconds doesn't turn the phone off, then try the rice bag method to dry out the phone. Normally, these methods tell you to turn the phone off, but if you are already out of warranty, I suggest keeping the phone plugged in and on, or else it may never turn on again if indeed the power button is completely broken.