The 5-year old controls the whole house when she antagonizes her sister. There must be some rules, because the 5-year old knows that her behavior will get her older sister in trouble. The 7-year old may be "intense" because she is constantly having to reassert her own rights and her personhood and her last ditch effort is to get violent.
Sit both girls down, turn the TV and all other noise off, and explain to them that what they are doing is not allowed. Look at each of them as you speak.
Tell the 5-year old that if she wants her sister's attention to wait until the commercial or the program ends to ask her question and tell the older one that hitting is not any way to solve a problem.
Make them acknowledge that they understand by repeating what you said to them. This is important because it reinforces what you are trying to do.
The 5-year old is learning that manipulation, which is a form of dishonesty, gets her her way, and she has learned to incite a fight to get attention. The 7-year old has been reduced to using violence to get her point across instead of using tact and the "system" to resolve her problems. Both these dynamics will come into play in these girls' lives down the line in negative ways. You don't want that for them. You are right to ask the question because you don't want this for them when they get older (or now when it affects your sanity!! LOL)
Explain the rules: the 5-year old is not allowed to interrupt her sister's TV program and the 7-year old is not allowed to hit her out of frustration.
Consequences:
SUCCESS
Set up a behavior chart for one week so the girls can see their progress. If they follow the rules, they will get whatever treat you think is appropriate.
Explain that this is a one-time treat earning opportunity. Using treats one time to teach good behavior is incentive. Using treats all the time is bribery and kids tune into that economic principle quickly. (It translates into blackmail by action.) Explain that once they have demonstrated that they have changed their behaviors to your satisfaction, you expect them to maintain that behavior. Oh, and no partial treats for partial compliance. This is all or nothing. It's faster and more effective that way.
Make sure the treat is equal for both girls. Kids have a very accurate, invisible "scale of fairness" in their heads.
FAIL:
If the 5-year old stands in front of the TV, she goes to time out until that program is over (1 minute per year of age rule is out the window except if it happens in the last 5 minutes of the program). She also loses one whole TV program for that day and has to go into time out for that period of time.
If the 7-year old hits her sister, she loses the rest of the program and another whole program plus goes into time out during that period, too, just like for the 5-year old.
Both lose the treat at the end of the week if they don't follow the rules. If one follows the rule and one doesn't, the one who succeeded gets her treat and the other does not. This is to teach each of them that they are responsible for each of their own behaviors and one cannot impact the other.
If the 7-year old comes to you to complain about her sister, drop what you are doing at that moment (although, it will probably happen the first or second time when you are in the bathroom - LOL) and handle it immediately. Every time. This tells both that you are serious about this rule. It is the fastest most efficient way to get your point across.
Keep a closer eye on them and try to catch the 5-year old before the 7-year old has to say anything. That conveys two messages: first, you are on top of things, and second, the 7-year old knows she is being backed up.
Explain the rule again each morning to them when they get up. This reinforces the rule and avoids the excuse of "I forgot." It also lets them know that you have not forgotten, either. (I learned a lot from my kids.)
If they don't get through the first week, do it again. Different chart. Same rules and consequences. Do not give a treat if they don't succeed. Parents sometimes make that mistake and kids will run with it.
I raised my three sons, each 2 years apart, alone for the last 13 years of their childhoods.
My rules: include everybody - no one gets left out even when friends are over (unless previously arranged); no name calling or hitting and ask to use someone else's toy before taking it; use good manners (please and thank you) and consideration for each other.
One time, they were all arguing and I grounded them from each other for an hour. They couldn't wait to get to play with each other again!
My sons are now grown - they got along for the most part when they were little and they all get along very well now. I am thrilled that they are friends with each other.