First, 35 mins for 5k is not that bad. I had my first sub 30 mins 5k run a month ago exatly on my birthday. I still don't run below 30 mins for 5k regularily - sometimes I'm able to, somtimes not. Friday I had 35 mins in 6m/km pace, which was nice.
Anyways, you need to slow down - I would recommend getting a running watch (I have TomTom Runner with hearth monitor built in) and pay attention on your pace - it should be fairly constant. 35 mins for 5k is 7 mins per km, next time you target for 6:55 and so on.
Another thing which I've read about is that you need to have at most 1 day in between. Your endurance start to fall off after 48 hours, so your next practice should be at most on the second day. Right now I'm preparing for a 10k race and I run on Tuestday (hills), Wednesday (easy run), Friday (harder) and on Sunday (longest). It sounds a lot (and it is) but its a good way to keep on working.
On more tip is that you need to rotate how hard your weeks are. I target to go up 3 weeks and then immediately go down a bit. So my Sunday runs go like this: 30-40-50, 40-50-60, 50-60-70 and so on. The idea is to give yourself some slack and more time to recover.
Finally, I find that having a clear go helps a lot. I always get more motivated when I have a race coming in. Right now I'm preparing for Cap10k and tomorrow is my longest pre-race practice - a whole 60 mins of running. That's one of my longest runs and frankly I'm a bit scared by it. But, I'll try giving my best and hopefully will be able to finish with 6:30 pace, which although doesn't sound much is good enough for me :)
Good luck with your training, endurance is withing your grasp for sure!