Orientation of Longi lr5-54hth-420m

No difference whether vertical or horizontal. Spacing avoiding vents and especially with mandated setbacks makes putting panels on a roof like a jigsaw puzzle. Roof space getts chewed up quickly.

IMO its best to group the panels together to leave open roof space for additional panels later.

The best installation angle of panels is neither vertical nor horizontal. It depends on the latitude of where you live. You can use Solar Panel Tilt Angle Calculator found online and install the panels on tilt brackets.

34°42'28"N 33°04'54"E is the approximate coordinates

Here is an equation created by Stanford University:

The best tilt angle(North)=1.3793 + Φ(1.2011 + Φ(-0.014404 + Φ0.000080509))

You may have a try.

The link of this theory: https://web.stanford.edu/group/efmh/...TiltAngles.pdf

Well, the orientation depends on your goals for the system. If your sole goal is maximum annual system output, panel/array orientation matters a great deal but there's usually more to panel placement/orientation besides maximum annual output.

Physical restrictions or conditions at the site or other considerations/mandates/restrictions such as from local jurisdictions will often affect panel/array orientations and/or placement. The goal often starts out with maximum annual output but that goal is often complicated/compromised/reduced by the other considerations.

But, first off, are you referring to the tilt angle of the plane of the panels relative to gravity or the orientation of the major axes of the panels ?

Also, what is/are the azimuth of the array panels ? That will have a bearing on the optimum tilt of the array, with the effect being larger for panels/arrays with an azimuth further off true south.

For an estimate of an array's performance try using the same PVWatts model as BryceFreeman/s referenced paper to get a decent first estimate of system output.
It's a user friendly model from NREL that's readily available on the net.
Read ALL the help screens first to understand what the model does and learn more about what you're looking for.
Get the required model inputs as close to your orientations as possible and do a few practice runs. Use 10% for the system loss parameter.
For multiple orientations do a run for each orientation and sum the results.

As a suggestion, I wouldn't take the results of that referenced paper as gospel or anything close to it. That paper looks like an academic white collar welfare project for a couple of struggling grad students. It might be worthy of an undergrad term paper. Otherwise, it's fluff.
The quality of the journal "Solar Energy" has dropped a lot since I left the Solar Energy Society and that paper is one example of why I left several years ago.

Take a few minutes, get familiar with the model and get your own results.