If you're not too confident with paying 90 bucks to replace the screen which might not even fix the problem I recommend buying a new phone as iPhone 5 is quite old now. And you may be able to spend a little more on top of 90 bucks and get a seller refurbished iPhone 5.
Have you tried a different cable and mains socket? If you have, then it may be the Lightning port inside iPhone causing the problem. It may also be the internal battery causing the problem.
You need to go to Toshiba support to download the drivers. Make sure to correctly select your laptop product line and model number. Also, make sure to download the correct driver for their respective brands. For example, if you have an Intel wireless chip make sure the wireless driver is Intel and not Atheros.
From the Apple TV Home screen, choose Settings > General > About and check the Model. Or look the bottom of your Apple TV device. Then compare the model number you see to the following page: https://support.apple.com/en-gb/HT200008