Are you home with her? Who is allowing her to watch tv all day? It's pretty simple -turn the tv off and redirect her to some type of activity. Go to a local park and play or get out the play doh, paper, scissors, glue and markers. Does she have toys? Tell her to play with them. Tell her you're making a new house rule that she can only watch tv for one hour per day. It's NOT good for her! Please do not think that just because something is animated, that it's okay for kids or good for them. "Family Guy," "The Cleveland Show," "South Park," "The Simpsons," "American Dad," and many, many more animated programs are for ADULTS -and very adult-oriented in their themes and language.My boys do watch cartoons, but it's limited. Whoever is taking care of her needs to have the television off for 99% of the day. She needs to be using her imagination and playing.
Also -she's 5. Did she turn 5 after the cut-off date for kindergarten? It would be really good for her to be at a preschool, even if it's only a couple of 1/2 days per week. There are many churches that have Mom's Morning Out programs like that. If you're home with her or if you have a caregiver staying at home with her, you can google classes like Gymboree, Kindermusik, The Music Class, etc. in your area where she could go once or twice a week. Local YMCA's often have great workout facilities for a very low cost. They usually have wonderful childcare centers for your kids while you work out, and many also have indoor pools where you can swim with your child and classes you can take with your child. Look for local indoor play areas as well. Many places have "bouncy houses/slides" for kids, and they'll also have some games and other toys. Usually in a big space with lots of room to run around -a place like that would be ideal for her. What about local children's museums? Those places contain hours of hands-on activities for young children.
I also notice you live in New York, NY. I know you may not be right in the city, but if you are -you have a WEALTH of museums and opportunities. Take her on regular outings to art museums (MOMA, Guggenheim, etc.) and to the Museum of Natural History. I'm sure there's probably a children's puppet theater in New York. We have the Center for Puppetry Arts in Atlanta, and they don't exclusively deal with children's programming, but they do a lot of kid shows. You may find a magazine for free at grocery stores and children's areas especially geared toward activities in your area for kids (we have several -one is called Atlanta Parent). Get one of those and find some things you two can do. Often people don't realize just how many free things there are out there.
If she is staying with a caregiver/nanny during the day, make sure that person KNOWS the new television rule! Make it a condition of their job! I would fire someone in a heartbeat who let my kid watch television all day.
Go to the local library! Find out all of their children's programming. They usually have story hours, etc. Plus, she can look at all the books she wants, go on the children's computers and play games at PBSkids.org and check out a few to bring home with her. Large bookstores like Barnes and Noble and Borders also have story hours throughout the week.
Take her to the zoo! If you can afford it, buy a membership and take her there once a week. She'll be fascinated at how the animals change and zoos offer tons of kid's classes and programs for kids. The same goes for local Botanical Gardens and any aquariums near you.
Bottom line -turn that television OFF! She'll get used to it -especially if she's engaged in something else fun. You may have to listen to some whining or crying for a little while, but don't we all? If she persists, simply tell her she will get 1 hour per day to watch cartoons, but if she keeps on crying and whining about it, you're also going to take that away and there will be NO tv at all. That always stops my 4.5 year old pretty quickly whenever he whines for more tv time! You'll just have to weather a period of adjustment.
Good luck! I always tell my boys that a little tv is fun and fine, but watching too much makes you slow and stupid, because it does. You are allowing her to make the rules at your house, and that's your job -not hers. I'm sure, like the rest of us, you have a lot to do and there are plenty of days you just don't want to deal with her, but when we become parents -we have to suck it up and realize that most of our time isn't ours anymore.