Baby can't stand to be on his own...

K
I'm having a really hard time. My son is 5 months old and very clingy. He will not allow me to put him down or get anything done. I've tried his exersaucer, playmat and bouncer. Nothing works. I try and just get small things like dishes done and he screams after only a few minutes. like a blood curdling scream.. it's upsetting because I just want to hold him but at this point I need to get housework done or even use the bathroom... Its impossible. Letting him cry a bit makes it worse. I feel lost and don't know what to do