Recently I bought an iPhone 5s used. Everything is working perefect even I can charge my iPhone 5s normally when connected to charger but the problem comes when I connect my phone to my macbook pro mid 2014, it doesn't recognize my iPhone at all...

Try closing iTunes, and then reboot the Mac and force restart the iPhone. Then try again.

To force restart the device, press and hold both the Sleep/Wake and Home buttons for at least 10 seconds, until you see the Apple logo.

I Don't think that anything in here is going to help, but take a look at it anyway. The only thing that I think it might be as for the suggestions in this support article would be to try another USB port and switch cables.

If you don't see your connected device in iTunes for Mac - Apple Support

I'm glad to hear that you were able to resolve it with a new cable.