What Are Normal Activities For 5 Month Old Baby?

My granddaughter is just 5 months old. She seems to have poor muscle control and strength. She cannot yet do a real straight-arm push-up. She has flipped from tummy to back a few times, but it is very inconsistent. I try to put her on her tummy but she gets very frustrated very quickly and just puts her head down and chews on her hands. I try to do this when she is rested and fed, but it doesn't seem to matter. Also, she can grasp toys held in front of her, but when she drops them she can rarely pick them up again. When on her back, she will turn her head to look at a toy but makes no real effort to reach for it. She seems to be within the normal range for height and weight and is growing. Should I be worried?