This assumes a median of 8 days from onset to death in the lethal cases, and a doubling time of # infections of 4 days, which seems to be around the current level for the world outside of China. The number is very sensitive to average lethality rate, and hence also to the age & health distribution of the population.
It's completely implausible that Italy has only 5000 cases, as people who have visited Italy for their winter holidays have very frequently tested positive after returning home. They haven't all randomly met the same 5000 Italians.