Is hers a full-day kindergarten program? Many kids, at five, still need more down time than full-day K allows (and rest or nap periods at K are just not the same as real down time or naps), but since more and more schools now have full-day K, I'll figure that's what she's got, and you have to work with what the school requires.
She likely is physically and mentally very tired.
When and where do her meltdowns occur?
What are the triggers?
If you sit down and think through it, there likely is some pattern to the times when she is more likely to have these meltdowns.
Do they tend to happen, say, in the afternoons right after school? She's especially tired and low-energy then (even if she appears to be bouncy or wound up!). First be sure to give her a protein-rich snack right away, even on the drive home from school if you pick her up -- I know that a snack in the car at pick up really made a big difference for my daughter and some friends said the same about their kids.
Then ensure that if she goes right home, she has a little down time before any homework she may have -- kids in K do have a little in many schools, but give her a short break. Don't let the break stretch out too long and homework get pushed too late, though. It should never be after dinner because dinner for a kid this young is pretty close to bedtime and she will lose all focus if she waits until after dinner (well, that's what I found at least). Be sure she has a good place to do homework that is away from her sister -- Big sister needs a space where she feels she can work without little sister being in her way or even in the room. Good light, all the materials ready, and never let homework drag on - if she has made an effort and seems stuck, she is done.
If she does not go right home after school, but goes on to an activity on some days -- I would look at her schedule to be sure she's not doing too much. If there is, say, a dance class or other activity immediately after school each week, see if you can shift it to weekends.
If she is melting down at bedtimes, again, be sure she wasn't doing any homework (however minimal - to her it's a big deal) too close to bedtime. Keep the bedtime routine she had before K as much as you can. If she regresses a little bit and wants you or dad to read a bit more to her, or stay after lights out -- do it. It will not make her babyish, or cause her to be less independent; it just acknowledges that she needs that little bit of extra time with you during a huge transition. It will not spoil her either; she'll get past it.
Is she melting down over things along lines of "I want what I want and I want it now" that she didn't used to do? Being more demanding since school started? Remember, at school she has to "hold it in" all day -- has to listen to and obey the teachers, and move from activity to activity when she's told without expressing that she'd rather do something else, etc. So she may be like a rubber band that's been taut all day, being ever so controlled, and home means she can suddenly let that tautness go -- and that leads to behavior you haven't seen before. It is a sign that she is comfortable and relaxed at home, which may sound odd since she's "disrespectful and dissatisfied" but she feels she can let go with you at home, and blow off all that tension from a long day of being on her toes. The issue is that the release of tension takes some forms that can't really go on too long. But rest assured, it's normal.
If her disrespect includes language (not necessarily "bad words" but ideas and images) that you have never heard before, it's possible -- not super likely but possible -- that she is hearing some new things at school from other kids, and if that's the case, you need to engage the teacher and express concern that she's coming home with some things she sure didn't bring in her head to school.
You can't let disrespect go, so at a time when she is calm and NOT just getting over a meltdown, talk to her in terms she can understand about how to talk to mom and dad. Tell her how when she talks that way, you cannot talk with her. Then next time -- walk away. Just say, "I can't stay and listen when you yell, so when you are ready to talk to me calmly I can come back." Go into the next room. If she follows you yelling or fussing, turn your back and do something else (washing dishes is good). If she persists beyond a second warning, institute a time out in a place that is not her own room -- an utterly boring corner or end of a hall, nothing else in sight. (See the TV "supernanny" Jo Frost's books for good advice on how to make time outs effective discipline.) If you have to escalate to taking away things she values -- do it immediately and calmly, not later and not angrily in the heat of the moment. And ensure that she knows in advance that time outs and/or taking things away will be the results of specific things she does -- do not surprise her with them or spring them on her! She needs to know that if she does X,, then the consequence is Y, every single time.
That's all about discipline but really if you also track the times of her meltdowns, keep her well fed, simply distract her if she starts asking for this and that and is building up to a fuss over "I want" -- that could help.
Do be sure you have a good connection with her teacher. Get to know the school counselor ASAP -- they can be terrific resources and are there for you, not just for your child! See the counselor and ask for ideas about how to handle her. This is what they're there for!