I guessed that based on the fact that your final lactate reading isn't especially high. A speed-based runner would generate higher lactate values at high speeds. Mind you, unless you were far off 15:50 shape at the time of the test, this session shouldn't have been all that demanding for you, with only the final 2000 starting to get "hard" and causing you to generate "a lot" of lactate. I almost withdrew my guess.
Your weakness is therefore likely a relative lack of basic speed/power. You would be well served emphasizing "speed" training a little more than traditional "endurance" training (long runs, tempo, fartlek, etc). Not solely speed training, but perhaps shift the balance in that direction. Lots of strides, and maybe 2 out of every 3 weeks some kind of truly fast work, like low volumes of hard 200s, 300s, 400s etc. Of course, depending on what phase of training.
Anyway, that's all I got for ya.