A. You've come this far, so my advice is to hold on a little longer. Your baby is on the verge of big developmental breakthroughs, and sooner than you think, he won't want you to hold him constantly. In the next few months, he'll master the arts of sitting up alone, crawling, cruising, standing, walking. By springtime, you may find yourself wistfully remembering the days when he just wanted to be held!
But you can't rush it. At 5 months, your baby really can't be taught to occupy himself for very long. Yet that doesn't mean you shouldn't put him down when you need to.
Go ahead and lay him on the rug on his belly with some soft toys to mouth while you pay a bill or two or do some other five-minute chore nearby.
Consider it his workout -- the neck and back muscles he'll be using to lift his head and chest will be valuable as he's learning to sit. If you put him down at the same time every day, right after his second feeding, for instance, he may even get used to it and not cry or whine for you to pick him up.
You might consider going about your household business wearing your baby in a front carrier (he's probably a little large for a sling to be comfortable -- for either of you). When he's too big for that, try a backpack. Use these gifts from the juvenile-products gods for as long as your baby (and you) can stand them.
A baby who likes to be held can often tolerate them for quite a while. Madeline, my eldest, enjoyed her front carrier until she was almost 9 months old and practically busting out of it.
I got to have my hands free, and the only downside was that her head always seemed to smell of vinaigrette dressing, an aroma that still reminds me of that brief moment in time when all she wanted was to be held.