Here are per-night homeless statistics from UN:
China has 2.6 million
Russia has 5 million
Ukraine 1 million
US has 554,000
But more profoundely, by homeless ratio, the US is not even close.
Germany, New Zealand, Czech Republic, Canada, the UK, Australia, Sweden, Luxembourg, Croatia, Bosnia, Russia, Peru France, Austria, the Netherlands, China and Greece -- ALL have higher homeless ratios than the United States. The US is in 33rd place for overall worldwide homelessness as a percentage of the population.
5 million figure for Russia for example appears on wikipedia  where it is cited from IB Times. IB Times cites Homeless World Cup as the source. Homeless World Cup cites the original IB Times article as the source for the 5 million number! This was the first number I investigated and it already seems super suspect.