1. I forgot to bring the camera.

2. I forgot that I would bring the camrea.
3. I forgot that I should bring the camera.
4. I forgot that I had to bring the camera.
5. I forgot that I must bring the camera.

(Does #1 mean #2, 3, 4, or 5?)

#1 could mean the same as any of the others, depending on the intention of the speaker. I see 1 and 2 as close to each other in meaning, and 3, 4, and 5 as close to each other in meaning.

The primary difference is in the meaning of the auxiliary verbs "would" and "must."

Based on the given options, in this context, statement #1 "I forgot to bring the camera" can be considered synonymous with statement #4 "I forgot that I had to bring the camera." Both statements imply that the person forgot the obligation or necessity of bringing the camera.