I would not force a child that young to take on lessons of any kind. It is certainly not only languages. Also in sports you see parents over pushing their children to become some miracle, child some child prodigy. Let these kids make sand cakes in the sand box, give them a break. 

At only 5 years old I doubt that the little one is reading yet so books would work if a native speaker were reading the books. Maybe there are some recordings of someone reading an English book OR... you could hire someone to read the book on a recording AND have a tiny chat with the little one too so that she knows that "Teacher so and so" is going to read us a book so that we can learn English together and then we can call and thank her. Something like that might be nice. 

With a 5 year old it's about exposure so anything that she likes and will do is what will work. KP was a strange kid :) ha ha and didn't like cartoons much, but there are people that learn entire languages just from cartoons. There's this dude that learned Japanese from anime and I'm learning to listen well to Spanish through Star Wars cartoons and bookbox and I'm an adult (maybe an adult with a simpler and more easily entertained mind than yours KP :D )

There are also songs. Songs are a wonderful way to learn! You could listen to songs with her and sing them together. 

Each 5 year old is going to be different too. I'm sure you will figure out something for her to be able to join in with your language learning and have fun with it. 

K.P. ... ane when the novelty wears off after a few minutes? Have you ever taught children?

That's sweet that you want to help your daughter to acquire other languages at a time when it comes so naturally. She could talk to the adults you are talking like she did because she wants to as long as they don't mind. If you could make play dates with children that speak other languages that would be great, but cartoons seem the very best at such an age to me because they are so easy, free and don't take any planning. It's a way to have a child entertained at a television or computer and actually HELP their future and their intelligence.  

I just LOVE the company Bookbox.inc. There are streaming cartoons in lots of languages with the words running beneath so that not only will she naturally learn to speak but also to read automatically, the way the best learning happens. She could watch the video in her native language once first to know what the story is and then watch it over and over and over again (like children like to do) in the target language.  

http://www.bookbox.com/

SeventeenSecond, Leigh Mumford, nobody said 'to force' or 'pressure'.  
I was forced to do a lot of things as a baby, some of them were probably harmful, some were useful, some battles I'd even won. But nobody ever forced me <em>to learn</em>:/ It's kinda 'force to breath' at the age.
Depends of the method used, of course, but it's generally not a problem to have children taught thing you know/use/love yourself. They want to know it!

Dorothy, it's a good question, how to design such a lesson.
In my (!) case cartoons never worked well (there were an educational course for adults by BBC and a cartoon by the same BBC. Both i'd found wery funny, both I watched, and learned really a little form them:) Just a couple of words. The same couple of words my parents repeated/talked about when they were watching it with me:-/ ).
I had surprisingly good times with the books. The books were in Russian of course, but some were about math. Which ruins my theory of interactiveness needed:)
Anyway, Skype can provide a lot of interactiveness. Kinda living people, nothing less. It's a great idea to use it somehow...

Alas, I can add nothing:( Maybe one can get the interior of both places involved? If a person from the other side of Skype and a child were <em>doing </em>things (even their usual activities), the experiece would come closer to 'real-life' one.

And there some universal ways to make a conversation more interesting. To pose simple problems etc...