Hello Jayden,
Thank you for the pictures, especially showing the measurements of the opening.
We do not have anything that large so you will need to modify the cutout to make it smaller. The Full Size Locking Steel Flush Door Latch # L3980 that you were looking at would be a great option, it would require you to modify the cutout to 3-3/8" x 4-5/8", it fits doors up to 1 1/16" thick.
The largest option we have fits in a cutout of 5-1/4" wide x 4-1/2" tall, and door width of 1-1/4"... view full answer...