Mother of three (mostly) grown children here. My kids came of age during the 90s, so I’ve been where you are, and I would strongly advise that a child of five not even be on the Internet at all, unless you’re prepared to sit there with her every moment that she’s surfing, or else you’re prepared to install a slew of Net-Nanny-type software, all of which advertise that it “won’t slow your computer down”, but which do, actually.
And Net Nanny can’t block all the websites that you would prefer your child not visit. There are some websites that are not necessarily XXX yet are still disturbing, that feature things like R-rated movie trailers and home videos. A Five is going to experiment with the mouse, and inevitably, one day when you’re on the phone or in the bathroom, she’s going to end up on a movie trailer website, and if you think cartoon blood and the F-word is disturbing…
Also, a Five isn’t old enough to understand, “Don’t click on popups that say ‘Yes’ without asking Mommy first.” I had a continual battle with MY kids until they were in their early teens and they could finally, at an adult level, understand the reasons WHY we don’t click on things without asking Mommy first. We had endless spyware, malware, Gator, and other odd programs installing themselves continually, all because my daughter in particular simply could not grasp, “When it says ‘click yes’, it doesn’t mean ‘click yes’.” And she was old enough to know better, too.
For “entertainment where you can park the kid for an hour to play in safety while you wash the dishes”, you need either videos or computer games *****, not the Internet.
And there is a ton of game software out there. Allow me to recommend Learn to Play Chess With Fritz and Chesster, The Zoombinis, and the I Spy series, for starters.
***** I’m assuming she has books, Barbies, Legos, crayons, paints, yes? 
