One of our daughters has behavior patterns like this. It may well be something completely different and I imagine there is a whole clinical taxonomy for these behaviors so one has to read answers like this for what they are worth, which may be very little, could be completely inapplicable in your situation.
That said, we don't think of our daughter's behavior necessarily as impatience. It is more a high degree of verbal interactivity, which is used in situations where she has anxiety about the future, about predictability, about transitioning from one activity to the next.
What helps us and her is to communicate- over-communicate- to her about the future so that going into a situation, there has already been a verbal interaction about what is happening next, and her questions have been answered, and she hopefully has acquired a mental model of what to expect.
In simple terms in the situations described in the question, before turning on the TV, have a calm conversation that is about establishing an expectation for limits that will be placed on the TV watching, and on subsequent activities.
The conversation protocol involves saying what we as parents expect to happen and getting her to say it back to us. "Honey, we are going to turn the TV on, and we are going to watch 1 program, then we are going to turn the TV off and do X. Does that make sense?" (She says yes) "So can you tell me what we are going to do next?" Then she will repeat back to us what we said we were going to do. Sometimes of course she will disagree and then we have to go into more discussion, explanation, negotiation- but exhaustive discussions are the usual state of play with 5 year olds. The important part for ours is her being able to use language to describe a plan for the immediate future.
When the program is getting close to the end we use reminders- "Honey, remember that we are going to turn the TV off when this program is over, and it is almost over. Do you remember when we talked about that?"
Or, before getting up to go to the kitchen, engage her also in thinking ahead- "Honey I am going to go to the kitchen, can I get you something?"
The reason I use the term anxiety is that this behavior is most notable before we are going on a trip and have to do involved preparatory activities like packing. She finds that to be highly stressful and we eventually figured out that describing what was going to be happening in exhaustive, structured detail, and answering her questions, was most helpful for her- and to us.
Hope that was useful, good luck.