I've had my LN-T5265F for about 9 years and never checked this thread until today.
What prompted me was a new Onkyo home theater receiver which supports HDMI (my old Pioneer, being a couple years older than the TV itself, had digital inputs but only coaxial and optical, which I used all the time). I always used HDMI with my TV through the TV inputs directly, and always experienced annoyances with the flaky connection, but it was always within the threshold of acceptability.
Now with the switching of HDMI inputs through the receiver, the HDMI issues of the TV kicked into high gear. So I downloaded the 1037 firmware update from a link in this thread and installed it.
The progress bar went to about 75 percent in 2 seconds, then got stuck there. After an hour I decided that the progress bar was not going to move any further, and had no choice but to unplug the TV. (It didn't respond to the remote or the buttons on the unit.) When I plugged it back in I was not sure what to expect, but to my delight it came back with the new firmware!
Now the HDMI connection is solid and my first impression is that the picture quality got better. My old firmware was 1009, and no matter what I did I could never get the black levels right without making the image too dark. Now I noticed that there's a gamma correction adjustment, which is great, but I didn't even need to use it because I was able to adjust the image (including black levels) without much effort using the other adjustments. This just wasn't possible before.
So I'm posting this in case anybody has a similar experience with the firmware update. If the progress bar gets stuck, don't panic. But do give your TV at least 60 minutes to make sure the update goes through.