It's nearly impossible to get a caliper on a mounted headlight housing however it's close to 5.25" so the 5.75" would be close to 1/2" too large to fit stock housing. You could save a few bucks by trying a LED H4 bulb with Hi/Low, they can be had for much less than the Harley lights. I replaced my stock bulbs with LED H4's about 4 years ago and they are still going strong. Only difference is that they didn't offer Hi/Low back when we all originally jumped on them. We all may need to update so find a good bulb and let us know.
Cheers.
Cheers.