Just to clarify for you, Nitrosomonas is the ammonia oxidising bacteria (AOB) found in our tanks, and Nitrospira is the nitrite oxidising bacteria (NOB) (I don't like that particular abbreviation for obvious reasons).
Nitrobacter is also an NOB, and is the one which was universally thought to inhabit our aquariums for many years until Hovanec proved otherwise not so long ago. Most literature you will read refers to Nitrobacter, as was thought to be correct at the time of writing. Only fairly new literature will speak of Nitrospira in our aquarium filters.
With regard to your cycling, I recommend that you should do large water changes to lower your nitrite to a measurable level. The AOB will turn 5ppm of ammonia into 13.5ppm of nitrite (the ratio of ammonia : nitrite : nitrate is 1 : 2.7 : 3.7 or to be more precise 17 : 46 : 62), so each time you top up to 5ppm and the AOB process that ammonia, you are adding another 13.5ppm of nitrite. As you can imagine, nitrite soon reaches 100ppm+.
If you have say 13.5ppm of nitrite in your water rather than 135ppm, the bacteria will process it back to 0 quicker, and thus a big water change will allow nitrite to fall to 0 sooner, speeding up your cycle. Leaving huge quantities of nitrite in the water only prolongs the cycle and is completely unnecessary. Your filter could already be cycled and you'll have no idea as it has such a backlog of nitrite to clear. You could be thinking the nitrite still hasn't moved as it is unmeasurable with your test kit and all you see is that it is off the scale.
I agree with Colin that cutting back the ammonia meantime will help speed things up too as it will minimise the build up of nitrite. Try topping up to only 2ppm once per day, and as soon as you see movement in the nitrite, crank ammonia back up to 5ppm to give the AOB time to catch up again (it will only take around 24hrs for the AOB to catch up again as they can double in around 24hrs).
Also, crank up the temperature to between 30 - 32C and maximise surface agitation to facilitate the best possible oxygen supply.
Hope this helps mate.
Cheers
BTT