Note that your statistic comes from a study of European cities, and is only true for Europe. By not noting that caveat you're implying world-wide, which is very much not true.
Nobody has studied Africa and India the same way, but it seems quite likely that the increase in heat deaths there will significantly the decrease in cold deaths.
> your statistic comes from a study of European cities
Yes, the ratio of 5 does (actually from Northern Europe). But if you look at worldwide data, the ratio is actually higher: 9.8. In other words, Europe as a region has a substantially lower ratio of cold-related to heat-related deaths than the world average. And Africa has a substantially higher ratio: 16.5 in Northern Africa and a whopping 58.3 in Sub-Saharan Africa. (Of course this is because the people there are so much better adapted to heat than to cold.)
Nobody has studied Africa and India the same way, but it seems quite likely that the increase in heat deaths there will significantly the decrease in cold deaths.