Yooper, I'm very sorry to hear about your FIL.

Diane, my DD was the same age, almost 4, when my dad was diagnosed with colon cancer. He had surgery two days after the diagnosis, so we didn't have any time to prepare DD. Of everyone in the family, I'd say she handled it the best. I just told her Pa-Pa was sick and had a boo-boo in his belly. We visited him at the hospital almost every day for six weeks (he got a hospital-acquired infection that was very serious.) The first time we saw him after surgery, she was taken aback, but in a few minutes, she was like, "OK, this is the new normal," and she was herself with Pa-Pa again. She just made herself at home at the hospital. She colored, chatted with the doctors and nurses, and teased her Pa-Pa. She brought him a stuffed animal and presents. Truthfully, at that age, kids are mostly all about "how is this going to affect ME?"

So I tried to keep it specific, like, "No, Pa-Pa can't play giddyup horsie with you right now, because his belly is sore. Would you like him to read you a story?"
Anyway, I just told her the truth without going into too much detail. (At 5 1/2, I would probably give more details.) I think it worked out fine.
Best wishes on your SIL's speedy recovery!