Hi Fiona,
Welcome to the boards.
I would definitely recommending shortening your A time, as at this age your A should consist of a quick nappy change, a song, or soft talking and then wind down to get ready to sleep.
The fact that your lo will not fall asleep in her moses basket could be because she is overstimulated and extremely tired. When a lo is overtired, this does result in short nap times. I would try aiming to get your lo ready to go down for a nap about an hour after her wake up time.
I would definitely persever getting her to sleep in her moses basket in a quiet darkend room, as this will make things easier when she is ready to go into a cot.
I would also suggest an earlier bed time i.e. about 7:30. You can cluster feed at around 5:30 ish, then bath as her A time, then the 2nd cluster feed after her bath then wind down and in bed for 7:30. This should tank her up until her dreamfeed at around 10:00pm.
At 5 weeks you can still expect at least 1 night waking.
HTH.
Paula x