is a scientific ground that a 1m loop would work well at 5MHz?
5 MHz is 60 meters wavelength. Any antenna with size 30 meters length or smaller will works.
The key point here is that signal level on the antenna output will depends on antenna size.
Smaller antenna size = smaller signal level on it's output.
And here is a limit of the signal level that we can receive, this limit is noise floor level of your environment.
This magnetic loop antenna works good with help of amplifier placed near antenna.
And because this antenna with amplifier is placed on a long distance from home and other electromagnetic noise sources.
Since home noises didn't affect it, the noise floor level is very low and antenna can pickup very weak signal.
But the problem is that this signal is very weak (it's level is too small). If you put it directly to the cable, you will not be able to receive it on the other side of cable, because it will be flooded with noise from your home environment. This is why amplifier is added to this antenna and placed directly next to the antenna. It amplifies the weak signal and when it come to your home through cable, it will be strong enough to not be affected by noise from your home environment.
This kind of antenna named "active antenna". And this is how it works. The key point here is that antenna together with amplifier should be placed on a long distance from any noise source, such as home or any kind of electronic equipment, power lines or just some piece of iron or some building.
The Near Field region of antenna is very vulnerable to any noise source. Because any noise source placed in the Near Field region will be amplified by antenna much more than DX signal. Since this antenna is too small in size, it's Near Field region will be not so large, and it helps to avoid catch noise from environment. Also, since it's small it has small gain, but small gain of antenna is compensated by adding amplifier.
The ideal distance [meters] from antenna to any kind of conductor or noise source is:
R = 2 * D^2 / lambda,
where D - is the size of antenna [meters], and lambda is wavelength [meters].
The wavelength can be calculated in the following way:
lambda = c / frequency,
where c is a speed of light:
c = 299'792'458 [m].
This equation works for almost all antennas. But
for small antennas there is a lower limit for Reactive Near Field region (the most sensitive part of Near Field region), for half wave dipole or similar antenna this lower limit is
R = lambda / (2 * pi). So, if you reduce your antenna size more, the Near Field region will not be decresed, and you will get just a smaller gain level of antenna.
For 5 MHz = 60 m, this limit is R = 60 / (2 * pi) = 9.55 [m].
It means that you're need to place your antenna at least on 9.55 meters away from any conductor, power line, building or electronic equipment. Otherwise your antenna will be flooded with noise.