I’m laughing hysterically at the idea of carrying off a ‘hiding quietly from granny’ strategy with 4 kids under 6 in the house 
Frankly this sounds like one of those times when a face to face with granny is the only way. Perhaps phrase it that your home can’t sustain another little one. The snacks, the loo, the toys, the cleaning, the refereeing etc.
Mention that in fact you’d been working up the courage to ask if she could pick up one/two of yours to take to her place on the days she has DN? Don’t worry, she won’t take you up on it. She’s shown herself to be overwhelmed with one.
Once you’ve set this scene, she’ll either figure out she’s been outsourcing ‘her’ childcare a bit and pull back or she’ll start to worry you’ll be answering the door with a relieved look, bag & babe.
Depending on your relationship with SIL, I’d be mentioning to her that you’re finding 5 a bit hard going. If she’s nice (or smart) she’ll have a word too. She’s not going to want a strop starting that could jeopardise the set-up for her kid.
You might need to arrange a semi-regular seperate grown up catch up with granny, to soften the blow. In all that spare time you have of an evening
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