Unless the S5 is VERY different than all other Samsung phones, that's either a defective phone or user error. Pressing a contact should just bring up the contact. To dial it you have to press the phone symbol by the number. I'd bring the phone to the carrier and let them see if you're doing something wrong, or if the phone has to be replaced (or reflashed, maybe).
Be sure to back up everything you don't want to lose, including your texts, pictures, videos and music. (Contacts that are Google contacts are backed up on your Google cloud account, which gets created as soon as you enter a gmail address in an Android phone. Your apps get backed up [these are the defaults, if you haven't changed them], but the data for the apps doesn't, so back up or export any game or other app data you don't want to lose. If they decide to replace the phone, all you'll get back is your SD card and, possibly, your battery. Any files in internal storage stay with the phone (for a few minutes until they do a factory reset, which they will do). If they reflash the phone, you may lose all internal data.
(And, of course, make sure all backups and exports are copied to a laptop, cloud account or someplace else other than the phone.)