It's tight.

The difficulty is in knowing exactly what will happen - there's nothing to prevent AC or BA from interlining your luggage, and there's nothing to stop them from reaccommodating you. But you're relying on an agent's goodwill to do so. So, the worst case:

Working backwards, T5 has a "conformance" cut-off of 35 minutes. Basically, unless you're clear of security by 11:05, you will not be allowed to go airside. OK, this isn't peak time, so you've got some advantage here. But let's assume it takes 15 minutes to clear security and 15 minutes to drop you bag (I'll assume you've checked in online). So that's 10:35 you need to be at Bag Drop.

T3-T5 landside transfer is by Heathrow Express train. It takes 10 minutes from T3 arrivals to the platform, the train runs every 15 minutes, and it takes about 15 minutes from Heathrow Central to T5 departures. So that's 09:55 you need to be landside at T3.

That gives you 1h20 to disembark, walk to immigration, clear immigration and collect your luggage.

If everything is bang on schedule, you can just make it. But it just takes one piece to fall out of line - delayed flight, long queues on arrival, secondary immigration, lost baggage, Heathrow Express problems, long queues at T5, and you're stranded.

This is the worst case scenario. Personally, I'm pretty risk averse wheat comes to DIY connections and will usually only do them overnight. Others are less conservative, and will leave 5 hours or so. 3 is pushing it, so I would try and figure out what your options are if you do get stranded - alternative LCC flights, insurance, etc, etc.