Here's my (former nanny) take on it:
-- and the other suggestions of growth-spurt was what first went through my head, so the remainder should be considered constructive, not critical of you or your skills...
He could very well be bored because he's wanting some peer interaction.
A couple of observations (I've worked with kids for 20 years now, so this is pretty anecdotal and empirical):
Kids at this boy's age need peer interaction, especially with other children who might play in a similar way. That means that neither you, nor little sis, are going to cut the mustard. Nothing personal--you just aren't a five year old boy.
Kids who have been 'entertained' a lot need to go backward a bit and develop their own entertainment skills. Do the children have Quiet Play time every day, or time for independent play, where they lead? I found, as a nanny, that while families love the idea of constant interaction, it's really not good for everyone. We needed breaks. Besides naptimes and quiet times (no media on during quiet time, everyone in their rooms, looking at books or playing quietly), I would also do up the dishes a couple times a day and keep the house tidied up, because it gave the kids a chance to go figure out what they wanted to do.
You list a lot of fun things to do: be sure to balance them with open-ended play and art opportunities. Personally, I found the projects in Parents/Family Fun magazine too product-focused and adult-led. MaryAnn Kohl has a great book called "Preschool Art" which you might check out at the library.... all of her books are great, so if that one isn't available, grab another. Here's the thing-- when kids are given raw materials and some tape or fasteners, they can really go to town all on their own. In my house we have a 'found objects' drawer which contains loads of paper towel/saran wrap tubes, container lids, cardboard of various thicknesses, (both from recycled cereal/dry goods boxes and backing from watercolor paper/legal pads), empty gift ribbon spools, small boxes, empty masking tape cardboard rings... all of these provide my five year old hours (and I'm not exaggerating, hours) of his own entertainment. Ask the mother of the family where you could set up something like this---
--- I'm going to interject a bit of opinion, which is this: kids get everything 'told' to them in so many ways. Their LEGOs come with prescribed designs and 'right ways' to make them, as do many of their toys. Keeping activities open-ended as much as possible will help everyone and give the children an opportunity to create freely.
If you can, also consider pulling back on as much media time as you can. I found while I was working with kids that the television and other distractions made them less motivated to go pursue their bliss because they were being constantly entertained by the tv and getting all the brain chemical signals (addictive, really) that go with watching the tube. As a preschool teacher, I could nearly always tell when a child had spent too much media time in the days before: I would hear "I'm bored" or "I don't know what to do"....and sure enough, I'd get confirmation from parents later in the day. (I actually started keeping track of the parents responses on this as a sort of experiment of my own.) Because I didn't hear these complaints often, when I did, it was noticeable.
I strongly believe that boredom is okay. It is, in fact, a chance for personal growth.:) *Just make sure not to solve the problem for him*. My sister does a lovely thing with her boys where she just sets up 'invitations' for her three... some playdough and a basket of tools on a table, a quiet place to work with some pattern blocks, some sticks and string outside, etc. (My found objects drawer is also an invitation of sorts.) A table with paper, a hole punch, markers/crayons, fasteners... this is an invitation.
So, with all that said, try to keep up some playdates with his school buddies, and then offer some fun activities which he can lead. Make sure he has quiet, media-free times during the day, and let him help you with tasks when/if he likes. I hope some of the ideas work out for you.
And ultimately, if you are offering a wide variety of things to do, at some point, the boredom is on HIM, not you. I would try very hard not to take the mother's comments personally.... if she's wanting you to be a non-stop entertainment for her kids, she's not doing anyone any favors. But it's okay for him to miss the activity of school. That's where he has a life outside of home, and that's okay too. (This is why many moms want to go back to work, so the feelings isn't bad or uncommon.) Boredom is not a bad thing-- it can be instructive if we let it!