LCD screen of Canon showing black in auto mode

Whether an image is automatically displayed or not following capture can be turned on or off using the menu on all digital Canon EOS cameras. If you have selected a setting that displays the image, you can also select from several options that determine for how long the review image is displayed. You may have turned it off without realizing what you were doing. The reason you see it when in the C1 mode is that the C1 mode was set up before you accidently changed the setting. When you turn the dial to C1 it uses the settings active at the time you recorded the then-current settings to C1.¹

You can turn image review on or off using the Shooting1 (red) menu tab of your camera's menu. From page 180 of the EOS Rebel T5/1200D Instruction Manual:

To control when the settings appear on the screen, use the Setup2 (yellow) menu tab of your camera's menu. From page 193 of the Manual:

For Live View, please be sure you have Live View enabled under the last tab of the Shooting (red) menu:

_{¹ This, of course, requires a Canon camera that offers user configurable "Custom" modes on the mode dial. The EOS Rebel T5/1200D does not include this feature.}