I have graphed this for the domestic terminal as a monthly percentage change from the previous year including a 12 month moving average. As can be seen growth in May was negligible compared to May the previous year and the lowest since 2011. That follows a period of consistent above average growth over the past year with the highest growth months around the total eclipse and also February, possibly related to Chinese New Year. There was also a long weekend removed from May this year.
Source: Cairns Airport
The international terminal is more complicated as there has been a reporting change for domestic passengers through the international terminal which has me head scratching a bit. However May was also very soft with a substantial decline from the prior month and soft on any comparative numbers. Total passengers lowest since March 2010.
My understanding was that some of the Chinese flights introduced last year were a seasonal trial (China Southern) for 4 months and not sure on what has happened there. As previously suggested the counter-seasonality of Chinese tourism may be among its most positive attributes.
Anecdotal reports seem to be mostly positive in recent weeks with the adventure festival and long weekend kicking early in June followed by the school holiday period so will await updated data from the airport.
Update: A response to a query from the airport the substantial fall in international passengers in May was mostly a result of Jetstar removing an A330 for maintenance resulting in flight reductions on the Japan route.