I'm confident I know what the issue is here - it sounds like you may have accidentally discarded the bin inner when emptying your machine. Without this in place, dust and debris will pass through the system and onto the pre-filter, rather than being separated from the airflow and captured in the clear bin.
The bin inner is the coloured cylindrical plastic section with a black rubber seal, which usually sits inside the clear bin as shown here:
If you've recently emptied your DC05 it's worth checking to make sure the bin inner hasn't fallen out. If you can retrieve it, it should simply push firmly back into place inside the clear bin.
It's also a good idea to wash both parts of your machine's washable pre-filter, as it may still contain dust even if it looks clean on the outside. Use cold water without detergent, and allow at least 12 hours for both parts of the filter to dry completely before replacing it in the machine:
I hope this helps. If you need any further guidance you're welcome to give the Dyson UK Helpline a call on 0800 298 0298. We're available from 8am-8pm from Monday to Friday, and 8am-6pm on weekends. Calls are free from UK landlines.
You may want to take the battery to a Batteries Plus or such - sometimes a battery will show voltage just fine, but choke once there's a load on it. They have the gear to tell (same as with car batteries)