Think about TSA's logic here:
Film under ASA/ISO 800 will not be affected.
You should request a hand inspection for film of any speed which is subjected to X-Ray surveillance more than 5 times (the effect is cumulative).

Seems to me that if 5 X-rays can cumulatively damage the film, one X-ray must cause some damage. And, how often do you see the X-ray operator reverse the belt to "take another look" at a bag? That may give your film a 2nd or 3rd dose on just one trip through the checkpoint. The OP passed through 5 airports, one of which double-screened all carryons. That one trip could easily exceed even the "safe" 5 X-rays. Because it is virtually impossible to know what future screenings your film could be subjected to, use a lead bag and always request a hand inspection. You might even consider developing film while at your destination. If the film was damaged, you might be able to replace some of the photos before you leave. If not, your negatives will be safe(r) on the trip home.