I realize they are all approximations, but nonetheless doesnt seem like livestock agriculture is in the top 5 in most estimations.
You posted that link first ;) That graph is accompanied by descriptions, which are helpful in deciphering it.
> total agriculture contributions as 18.4% of total contributions and livestock at 5.8% total contributions
"Livestock & manure (5.8%): animals (mainly ruminants, such as cattle and sheep) produce greenhouse gases through a process called ‘enteric fermentation’ – when microbes in their digestive systems break down food, they produce methane as a by-product. This means beef and lamb tend to have a high carbon footprint, and eating less is an effective way to reduce the emissions of your diet."
"The overall picture you see from this diagram is that almost three-quarters of emissions come from energy use; almost one-fifth from agriculture and land use [this increases to one-quarter when we consider the food system as a whole – including processing, packaging, transport and retail]; and the remaining 8% from industry and waste."
So those 5.8% are just gases emited by those animals / from manure.
We'd have to add a part of land use, deforestation, wastewater, chemicals and energy to get the complete number.
The page was written in September 2020; we have more recent studies, I've posted one earlier, which gives the potential range for animal ag. between 16.5 and 28.1%.
https://www.researchgate.net/publication/352100490_Emissions...
https://thebreakthrough.org/issues/food-agriculture-environm...
In 2013, the Food and Agriculture Organization of the United Nations estimated that livestock production accounted for 14.5% of global greenhouse gas emissions. Though the analysis was based on data from 2004 and 2005—over 15 years ago—it remains the most widely cited estimate of livestock’s global carbon footprint ...
More recent data and science indicate that livestock may contribute a wider range of emissions, potentially more, potentially less. For its part, the Food and Agriculture Organization of the United Nations has released a new, lower estimate that livestock produce 11.1% of global greenhouse gas emissions. Peer-reviewed studies have put the figure higher, at up to 19.6% of emissions.
...
Ultimately, it’s unlikely that researchers will agree on a single estimate of livestock’s global contributions to climate change. That figure is a moving target, shifting depending on the year, the method of estimating the warming impact of methane, and many other factors. But one thing is clear: we won’t be able to avoid the worst impacts of global warming without tackling emissions from livestock.