Agree, might be teething starting. Is she also red in the cheeks, dribbling loads, or stuffing her hands in her mouth? If so, maybe try a wee dose of calpol and see if she cheers up....if she does, then there's your answer! Teeth!
Also, I have to say this was a bit of a miserable grumpy age for my DS...he couldn't sit up, or do anything yet and I think he was reall bored and frustrated at being a baby! He enjoyed a 10 minute stint in a door bouncer at this age, and I borrowed a jumperoo which used to buy me 10 mins of quiet!
I also read loads of colourful story books with him and i have to say let him watch 10 mins of Baby TV (sky channel 623) a couple of times per day on my lap. I never really got into the whole babywearing thing but if that's your bag then a sling might help too?
I have to say, from this age onwards I started going out the house twice a day with my son. Every goddamn day. And I still do now at 16mo. He just gets incredibly bored and frustrated at home (we live in a small flat which doesnt help). So at that age I started going to various mum and baby groups at various local church halls, just being in a different room with different toys/people to look at seemed to cheer him up a bit. I also started cheapo swimming lessons (basically singing nursery rhymes in the kids pool) at the council pool once a week, and as the weather gets nicer you can go for a walk in a park once a day. In the meantime a stroll round some shops? Local libraries often do free 'rhyme time' singing sessions too...at 5mo she might just be old enough to appreciate a few rounds of the wheels on the bus?
Once your LO can sit up properly you can do more (a trip to the swings, plonk her in a trolley and walk around tesco - ds still loves a trolley ride), and then once she can walk it will get 100% easier. DS is a boisterous toddler now but it is SO much easier than when he was a miserable baby!! We can do things now....pick up leaves in the park together, soft play, walking around the fish at the local garden centre, toddler groups. It DOES get easier. You just ave to hang in there if you have a bit of a grumpy baby. And try not to swing for those mums with placid contented little babies who sit there chewing their fists all day :)