I do not use the 0 and 5 method, not for at least 4-5 years for the reasons Rafal points out. I noticed this visually apparently Nicholas Linden has backed this up with sensitometry, which btw is not my strong suit. I use it for calibrating processes and then move on to my eyes.

It should be pointed out I am a big time fan of Ilford Warmtone, and now Art 300 which I believe is the same emulsion.... All my comments are directed at this paper .

I have printed now in two eras... 1 era where there were only graded papers... 2 era where we have Ilford Warmtone ...

I switched to this paper for a specific reason... my clients liked the prints better...

Era 1 I remember the days of two bath dev, hot dev tray off to the side to help in the burning in... if you wanted an overall strong contrast print you would move up to a grade three or four and suffer the crazy amount of burning in the highlights.. which after time just got soft and flat/muddy due to the silly burn time, not to mention the fact that the burns could become obvious.

Era 2 I lay down an initial tone which puts inertia in the highlights and defines a long tonality print.. I then use the grade 5 filter to increase Dmax and contrast to taste.
I will burn the highlights with low filter and 5 filter, usually this burn is very insignificant and does not soften/muddy up and the blacks within the highlights are more defined and create the illusion of tonality.

I prefer Era 2 printing which is this controlled mix of filters..
I use an 80% density rule for the first filter .. in other words I make sure that I am 80 % happy with the density of the upper highlight region and I dodge the shadow regions to make a pleasing print... softer but nice ... think Jock Sturge's print a bit light , a bit soft, but nice blacks starting to emerge.

Then with a second filter 5 I hit the timer either once , twice or even more to determine the overall final look ..

During both filter exposures I am dodging to control local areas.

I use the 00 and 5 for burning in areas that I want to make sure are in the print for aesthetic reasons. I do not like paper white within my images but prefer to see the easal blades lines as a guide for blank sky tonality... If I do not see the separation then I know I need more tone.

WHAT METHOD AM I USING as I do not like the 0 and 5 method, and I do not like the single filter method...

Until someone can give it a name I will call it a MODIFIED FILTER METHOD... using the outflanking method to determine initial exposure... and 0 and 5 burning in for aesthetic reasons.

Its no wonder the OP is getting confused,,, the cat is looking better each day btw,, To be fair to both camps , the image supplied would work in Era 1 or Era 2 with not too much issue.

I just use the MFM method now for all printing as it gets easier over time.