Pretty decent run, though it can definitely be improved. You can save ~0.5 seconds if you jump up the right side at 4:45, though it can be a bit tricky to get. However, since the intro to this level is quite long, it's not very fun to grind for. So I'm certain a 5:16 is possible, but that's for some other time.

Also, since you don't need to kill any enemies in this level I take the Dexterous upgrade, as it speeds up the pickup animation for the pistol by 13 frames. Normally it takes 55 frames, but with the upgrade it only takes 42, so about 30% faster from my testing. Not much, but every timesave helps.