This page of our guide to Life is Strange True Colors contains a description of Part 2 of Episode 5. It covers the visit to the hospital and the meeting with Alex's mother.
You'll wake up leaning on your brother's shoulder. He'll wake you up and start a conversation. He'll tell you where you are, how old you are, and what you need to do.
You need to go to your mom and repeat what you did years ago. Only this will allow you to move on. If you fail to complete the task, Gabe will have you repeat this part of the game.
Let's start with the fact that there are several documents and secrets in mom's room. Examine every nook and cranny carefully to recall as many facts about those times as possible.
You need to pay attention to the water, it's very important.
Go to your mom, talk to her, and she will start coughing. You need to get her some water.
The water's on the counter. All you have to do is go and get it, and then help your mom drink.
Alex's conversation with her mom will be short, but also very painful. During the conversation, Alex will receive a gift from her mom, which is a very important element in the story.
This part of the chapter will end with Alex's outburst of sadness. There's nothing you can do about it. It's a scene you can't skip in any way.