Hi - My children are much younger than your eldest, but I have some suggestions you may find useful. I also agree that homeschooling is a great way to foster meaningful relationships and interact with a variety of ages and personalities in a more approachable, less threatening way.
First, be sure to take time to deschool. The general rule of thumb, if I recall corrrectly, is one month of deschooling for every year a child was in school. This doesn't mean that your daughter won't learn anything or accomplish anything academic, but instead she will, hopefully, have a chance to get out of the mindset of school/learning = drudgery. In other words, don't fall into the "school at home" trap. Find a local homeschool group and make library dates, park dates (if the weather is nice), meet at museums, etc. Does she like to dance, are there any dance classes offered by your local rec. centers? In my area, the rec. centers offer a full semester of dance classed for $35.
If you do feel the need to do academics, consider basing it on her interests. What books does she gravitate toward at the library? Use them as platforms for "casual" discussion. Play games she enjoys, even if they are below her skillset - the point is learning is happening in a non-intrusive way. Have her help plan her curriculum and schedule; give her some control over what she learns and when.
The Charlotte Mason approach is also nice, especially, if your daughter likes to read. Lessons in CM are kept short, 15 - 30 mins. with time increasing as the child gets older or the material more difficult. Spending lots of time outdoors, is also a large part of CM. Checkout Ambleside Online or Simply Charlotte Mason dot com for more ideas.
I also encourage you to find out what your daughter's learning style is and your teaching style (if haven't already). This should help you decide what approach might be a happy medium for you and your daughter if your styles are different. For example, since you are busy with four other children, you may not want to use curricula that requires you to set up lots of materials, etc. Or if your daughter doesn't enjoy reading then you may want to limit that part of the CM approach choosing instead to read to her or use shorter books, perhaps with large print, for example.
We are ecclectic schoolers in my family, primarily child led and I tend to ignore age and grade leveling, choosing instead to focus on ability and provide materials at the level my kids seem to be at and slightly above that to provide some challenge. We also use the Thomas Jefferson Education Philosophy (tjed dot org) and do a modified version of "reading, writing, and discussing" taking into account that my daughter is still young and lots of writng tires her out.
I hope this helps (and makes sense).
Mizzou
