I have to lean towards Sweet Violet's advice. I am raising puppies without their momma, and I know they need more human attention than normal because they are not getting all the mothering they would normally receive. Seems like I am always feeding them, or getting them to go potty but still I try to hold each one several times a day just for loving, stroking them and cooing a little, close to my face, just so they know they are getting some attention.
They also like to be warm. If they are the least bit chilly they will start to whine. Do you think your little one is always warm enough? I have to watch the A/C temp here but I know some parts are still having cold weather and the floor can get colder than the rest of the room. Maybe a sweater?
I bought a plush kitty from Petsmart that had a little heartbeat thing in it and these large handwarmer like packets. You shake the packets and they get warm and stay that way for 20 hours. You put the packet and the heartbeat thing in a little pocket on the bottom of kitty and the puppies have a nice warm, heart beating snuggle friend for when you are not there with them. My puppies like to snuggle up close to it and sleep.
One more idea -- maybe you should have your puppy confined a little more? I don't think 5-6 weeks is old enough to have the run of the house. That big of an area can be overwhelming to them and a more confined area could giv ea sense of security.
Once they are 12 weeks or so, then I would say, yes, you would need to be careful about giving in to every whine to be picked up. But for now, being a "Velcro baby" (I love that term) is not a bad thing. I also love the idea of a sling, and may see if I can fashion something like that so I can tote mine around. We have to give them a lot of loving to try to make up for their momma not being with them. If you watch a new mother dog with her puppies, they are constantly licking on them, showing them they are there. I draw the line on licking on them

, but am willing to give a lot more attention to them than I would most new puppies.