I also don't agree with the comments about not using arm bands in future, or of commenting on bad choices at this stage. I would probably say you'd like to go swimming with him again, but explain why it caused a problem that he wouldn't get out, give reasons, explain what is expected. Arm bands are needed for safety but also allow the child to move arms and legs to swim and the alternatives - the float or vest - won't be as good afaik. I would just buy new ones this time - unless he didn't want to wear them hence the biting them, in which case maybe let him play without them in his own depth for a while.
If your child is not used to swimming they may get exhausted quickly/be in need of something to eat which means they are more likely to meltdown.
You can think about whether you stayed in too short a time or too long a time.
Before picking him up did you give him quite a number of chances to walk out on his own, and give good solid reasons for why it is time to go, reassure him that you can go swimming again soon, and so on, and finally as a last resort give fair warning that if he continued to ignore you were just going to have to carry him? I wasn't sure from what you'd written.
Most 5 year olds require a fair amount of background management and patience, even those from secure backgrounds.
The fact that there was less violence towards you is fantastic.