I had it on my iPhone 5 too. I mean "clicking" sound and feel when slightly pressing home button on the sides. I recognized it after 3 months of use. Had quite same on iPhone 4 when probably displey cleaning solution and finger grease leaked into it. Felt like home button is not going up and down 100%. Like it stickes to glass edge a little... Clicking when slightly pressed. I fixed it by washing the button
Recognized same on my iPhone 5...did the same. Feels OK again!
I washed it with small droplet of DESTILED water "massaged" around edges into home button, clicked several times on every side... Kept iPhone turned off for three hours... It has been two days and button feels solid again. No clicking feel when touching.