I'm not sure where you live, but at solstice time, I never get enough sleep and wake up cranky every morning. It's not fully dark until 10:30 and it's getting light at 4:00. So if this is anything like in your area, I would wait to blame anything IN and around the house for this until later in the summer when nighttime is longer. In fact, I notice a peak in comments about sleep right around both solstices.
But other than that:
We don't have story time in bed, we have it on the couch. We don't go straight from stories to "lights out" (which is meaningless this time of year anyhow), but after stories we brush teeth and get jammies on. Beds are only for bedtime (or toy "festivals" during the day, but not stories.)
It can also be the content of the stories. I don't fall asleep easily because my mind is forever racing. Scary or not, if it's a story worth thinking about maybe she's thinking about it too much. Another reason to separate the stories from "lights out". 5yos are starting to get a grip on real/pretend (though it's still shaky), are more likely to contemplate the story after ward, and are ideally suited to expanding on the story in their minds. (Growing up, this was what I did after I turned the lights out--play pretending stories in my head and whispering to myself. I'd be awake for hours sometimes!)
I would not use "cranky in the morning" as the sole guide to deciding is she's getting enough sleep. (Well, you mentioned length of sleep, but I've always been dismayed how little sleep my kids need compared to me.) *Where* in your sleep cycle you wake up is a big deal as well. Some of us wake up cranky because morning is our deepest sleep, and we are getting up from that instead of the REM sleep more amenable to gradual waking. And some of us (again--that's me!) are cranky risers anyhow. My daughters are, too, and they sleep just fine. We just have to avoid "throwing our grumps around" until we all wake up some more. First thing in the morning is when I have always done TV time because I am a crab, they are crabs, it's just better this way (and when I would limit TV strictly it was easier just to get it out of the way.)
My girls often sleep in better if they've used the potty at night.
Finally, completely out of the ball park, does she wake up ravenous in the morning? Could be some blood sugar issues if so.
"She is a mermaid, but approach her with caution. Her mind swims at a depth most would drown in."