
Every five years, the United Nations Population Division publishes datasets estimating international migrant numbers.
The three countries with the largest emigrant population increases in each five-year period since the UN began records are below, with emigrant population increase in brackets (in millions):
1990-1995: Mexico (2.6 m), Rwanda (1.5 m), China (0.8 m)
1995-2000: Mexico (2.6 m), China (0.9 m), India (0.8 m)
2000-2005: India (1.6 m), China (1.5 mil), Mexico (1.3 m)
2005-2010: India (3.6 m), Mexico (1.6 m), China (1.4 m)
2010-2015: Syria (5.4 m), India (2.7 m), China (1.5 m)
2015-2020: Venezuela (4.7 m), Syria (2 m), India (2 m)

Which country will have the largest increase in its emigrant population between 2020 and 2025, according to UN data?
Feel free to add other countries.
The UN data for emigration can be downloaded from their webpage, see [Total, origin] under the header Data. To obtain the five-year difference, one will need to manipulate the data by deducting the more recent year (e.g. 2020) from the previous year (e.g. 2015) for each entry in the tab named Table 1. For example, this is the top 20 countries by 5-year change after I manipulated the data in this way and sorted by largest 5-year change between 2015-2020:
See Our World In Data for the data in a user-friendly form.