I can't use my speaker phone while in a phone call on my iPhone 5S?

I recently got an iPhone 5S and when I call someone (a normal phone call), it won't allow me to click on my speakerphone button. It's not that it doesn't work, I'm just unable to use the function while in a call.

Try restarting the phone to see if the button will then work. Also check your headphones jack. Pocket lint and dust are notorious for falling there and making sensors 'think' that a headphone set is attached rendering other normal features useless. A puff of canned air in the hole works well. If these two don't work, put the phone back to factory settings.
Best luck.