My PNY 32 G flashdrive will not copy a 4.8 G file from my harddrive, saying it is too large. Flash is empty. How to fix or go around this?

I just bought a new PNY 32 gig flash drive. I tried to copy a 4.85g file to it from my iMac hard drive. It starts to copy then gives a message the file is too large for the drive format. I had loaded it with about 18 g of files yesterday, copied those files to my MacBook then trashed and erased them from the flash drive. I checked both the flash drive and the file it would not copy using Get Info. It said the capacity of the flash drive is 32.16 G and available is 32.01 G. It says the size of my file is 4.85 G.

Another strange thing that may or may not be related to this problem. When the icon for the flash drive appears on the screen, I click on it and open it, and it displays the contents of the hard drive. I found if I moved a file from the flash drive display to the trash, it disappears from the hard drive listing. I can then rescue it from the trash and put it back in either the hard or flash drive folder and it appears in both.

I have another 32 G flash drive, different brand, which acts normally, except that it also will not copy some files that are smaller than the available space, again claiming the file is too large.

Anyone have any ideas what causes this anomaly and how to fix or get around it?