The iPhone 5 was released in September of 2012, discontinued in September of 2013 and succeeded by the iPhone 5C and iPhone 5S, both released in September of 2013. The iPhone 5S was replaced by the iPhone SE, released in March of 2016.
The glass screen and LCD are the most common things that break and shatter on the iPhone 5 series. If you have dropped, broken, shattered, or cracked the glass screen on your iPhone 5, 5S, or 5C, the proper repair is replacing the iPhone screen assembly. The cost to repair your iPhone 5, iPhone 5S, or iPhone 5C screen is listed below and includes the OEM replacement part, labor, and a 90-day warranty.
Make sure your iPhone shows up when connected to iTunes or you may have other issues.
Since your checking your charging port, consider backing up your iPhone in iTunes before bringing it in. Better safe than sorry.