All About SingleMother : Baby 5 Month Development ( fisher-price.com )

How your 5-month-old might play now

She can reach out and grasp toys
He smiles at other babies—and his own reflection!
She can now "multitask"—for example, babbling and reaching for something at the same time
When offered a toy, he adjusts the position of his hand to accept it
She can roll from belly to back
To explore his world, he begins mouthing objects

Toys that help develop a sense of self

Start by exploring. Hold your baby on your lap and position the toy in front, like you would hold a book. Explore all sides of the toy with your child and describe what you see as you go.
Who do you see? Initiate baby's sense of self-recognition by pointing to her reflection in the mirror, then to your own. "Peek-a-boo! I see you. Do you see Mommy? Who else do you see?" And point out your facial features. "See my eyes? Do you see your eyes? Here they are!" That's how connections begin for babies.
Tummy time is important for developing neck and torso muscles. To encourage your baby to play on his tummy longer, give him something to look forward to by placing the mirrored side of a toy within arm's reach.

Infant play gyms

What do you see? Get down at floor level to get baby’s view of overhead toys. This will help you know where to position her for the best vantage point. Change your baby's position every once in a while to freshen the view.
Play together to encourage communication and add fun to playtime. Pick a time when baby is in an active play mode, not sleepy or hungry or overly stimulated. You'll be able to tell; if the toy looks too busy for him at the moment, he'll close his eyes.
Talk about it. To help your baby learn there's a connection between words and actions, move the parts and talk about them as you go: "Shake-shake-shake. See the silly little face smiling at you?"
Hum or sing along to the music on the gym and point out light-up features. The more you talk to your baby and directly engage him, the more you're benefiting his development.

Activity toys

Touch and try. Invite your baby to explore all the features of a toy by going through them together, helping him feel the different textures and activate the sounds and movements. All of this sensory stimulation prepares a memory bank of experiences that will continue to grow.
Playtime, anytime. Let baby enjoy activity toys with lots of colors and actions that tempt her to reach out and touch. This will enhance eye-hand coordination along with thinking skills.