Grease wont hurt it your 5906 one bit and it stays in place better than oil so one can argue it might be better. Any quality grease will work, I've used gunslick, slide glide (in all 3 viscosities), shooters choice, frog lube paste, and imperial action wax (discontinued). It all works well on my PC1911. I just kind of slather it on, reassemble, and hand cycle a number of times, then wipe it all down to get anything that oozes out.
For the 1911, lube it good and then shoot it till your hands hurt. Relube and enjoy.
Forgot one caveat with the grease, if you live in a cold environment where you typically are below around 55F stick with a quality oil. Grease can thicken up slowing the slide resulting in jams until it warms.