This is fairly common.
Bear in mind, that "fears" in children, start from about 2 years old, as well as night mares etc.
It is because, their imaginations and cognition, is changing.
And "fears"... will manifest itself, differently, per age.
Even 8 year olds, have fears of night time or "monsters" or of the dark, etc.
Your child is not unusual.
Both my kids, have had spurts of being JUST like your daughter too.
And my kids are 5 and 9.
Bear in mind, that kids "fears" are just generalized or just childhood stuff.
So they may not be able to tell you SPECIFIC things, like an adult would.
They are young.
To a child, "monsters" are anything scary.
I had those too, when I was a kid.
Your child does not seem extreme to me.
And yes, children get more attached or less, per age. My son is 5, and he is again really attached to me. No biggie. It is a phase. I know that so I take it in stride. He was like that at 3 years old too.
What you can do is, just tell your daughter that if she is scared of something, she CAN tell you. Instead of screaming it.