Hi again builder,
Those PSA values look pretty stable over 10 months, though elevated of course, and up from that fairly reassuring 2.6 level three years ago. From what you describe, I can see why your doctor was focusing on an infection as the cause.
It gets to be a tough judgement call: go ahead and have a biopsy, with a strong chance there is little or no cancer and that the result will be negative in either case because either there was no cancer to find or the core was not taken where the cancer was, but with a chance of finding cancer, or hold off on a biopsy with a small but definite possibility that any cancer could gain more of a foothold.
Here is what stands out to me in what you've written, mostly on the good and hopeful side.

On the good side, the PSA is quite stable over ten months, assuming the same lab had the two readings in the 4 range and another the two in the 5 range. The difference between the labs could be the use of different PSA tests that check different places on the PSA molecule, and it could also be due partly to different lab procedures. The slight variations, including what looks like a downturn from 5.4 to 5.1, could be due to your own day-to-day variations in PSA production. That's not the way PSAs generally behave (stable or a downturn) in response to prostate cancer, but it is one of the patterns consistent with infection, perhaps boosted by enlargement, as I understand it as a layman. That said, cancer could still be there.
Also on the good side, you have had strong evidence of an infection at work previously, and have good evidence that there is still something other than cancer going on, which would influence PSA (causing it to be higher than it would otherwise be) and free PSA (causing it to be lower than it would otherwise be). I've read that many of us who are in our 50s or older have some degree of prostatitis.
Again on the good side, that negative DRE.
On the negative side, you have a PSA somewhat above the old cut off of 4 and a rise of more than 2 over three years.
Did your urologist indicate the current size of the prostate? The rule-of-thumb, based on research, is that healthy prostate tissue makes about .066 units of PSA for each cubic centimeter of prostate. It would take a quite large prostate of about 71 cc to explain all 4.7 units of PSA, but it's possible you have both a somewhat enlarged prostate - not surprising at age 55, and some infection, each contributing to a higher than expected PSA. Of course, there could be some cancer in the mix too, but if so, it might be a lot less than just the PSA would indicate if there were no enlargement and no infection.
Have you considered a PCA3Plus test? That is increasingly being used to help separate the PSA sheep from the PSA goats and can help in cases like yours.
Have you considered taking finasteride for six months to see if your PSA drops by half or more, which would suggest something other than cancer? Finasteride is proving useful for prostate cancer treatment, as I see it, but it was approved to treat enlarged prostates. (Just this spring there was a presentation at a major urologist conference that again pretty much proved that finasteride was safe - not fostering high grade disease but rather making it easier to detect.) Avodart would probably do about the same thing. However, infection might throw off these results too. At least you would have a good shot at taking care of any BPH.
You could also adopt nutrition, exercise and stress reduction tactics that appear to substantially help prevent and support treatment of prostate cancer.
Trying again to identify an infection might work.
Of course, having another PSA test in a month or so and watching for any change is another option.
It's easy to view all this from afar. Not so easy when you're in the hotseat and need to decide what to do.

Good luck with it.
Jim