running: higher heart rate when slowing down?

Forget HR zones for now...what does your effort feel like when you do your 5 mile runs? By definition, you can only sustain zone 5 efforts for 3-6 minutes. If you are really running that hard, every run you do should feel "hard" to you. Do they? Or do they feel easy and relaxing?

Everyone will gravitate towards both a walking gait and a running gait that is the most efficient for them. Going faster or slower than this natural pattern will require frequently result in a higher HR.

My guess is that your 5 mile runs are being done at a fairly easy to moderate pace for you, so slowing down is going to be hard.

on the other hand if every 5 mile run you do is at a race pace effort...slowing down should be easy.

My question for you would be, what are your running goals and why did you decide to slow down your runs? If you feel that you are running too hard, you should just go out and do a field test or a 5k race and get some HRs adn paces to train with adn see how that goes.

By that definition, I'm not in zone 5. My runs aren't "easy"; by the end, I'm fairly gassed, but they aren't at race pace, either.
I attempted to slow down because I've read training runs (base miles) should be in zone 3. I think I'm definitely running harder than that.

I notice that at any sustained effort that's above the middle of zone 3, that upon slowing or stopping my HR will jump a few BPM for 10-20 seconds before beginning to decrease.  Could that be what you are seeing?

It's really hard to imagine you slowing down your run and it resulting in a sustained increase of your heart rate.

Can you be specific about the 2 running speeds you are referring to, and the HR you are seeing?  ie. "8:00/mile pace is 148bpm, but 9:00/mile pace is 153bpm"

My last 2 runs were both about 5 miles. The first was 8:48 at 155 bpm. The second was 8:19 at 150 bpm. The second run was actually more hilly, also.

Oh, I see.  These were different runs.

Well, there are a lot of factors that can vary day to day that have an impact on heart rate.  I don't know how many times you've run this experiment, but your heart rate can and will vary based on the time of day, hydration level, how recently you've eaten, caffeine intake, how well you've slept and what your recent training load has been.

If you were to compare the two running paces over time and determine a consistent correlation (big if), then I would suggest that the differences are small enough to potentially point to a running economy difference.  I would find it curious, but not shocking if your economy was noticeably worse at the slower speed.

That question aside, do you know what your LT heartrate is?  Or your max?  150bpm is fine if your max is 200+ or if your LT is 180+.

Most of my easy runs are in the 130-140bpm range and it works very well.  If you can slow your pace down to that HR it would be advisable. 
Have you plugged your numbers in to the McMillan formula to get your training paces?