Machinery Exp
You can get to level 5 Machinery without Confucius Temple. The easiest way to do this is to gain initial machinery exp by getting access to Dirty Street in Chuxiang City I believe.
The leader gives 600 Machinery exp. Then I went to the Tomb Raider Sect leader and got 1800 exp from him which gets you to Machinery level 3. Then to get archive books for the water bandit girl you go to the dragon library which I believe is also in Chuxiang.
You can buy books to give to her. Then you go all the way to the water bandit hideout and get that 1800 exp which gets you about halfway to level 4. Finally you need to get to level 55 and at this point if you are part of the Unparalled Sect with the old man (this may be possible with other sects but I haven’t joined any other sects yet) he reveals the location of longevity tomb (great place to grind levels from 55-70). If you open all the chests in the tomb it will get you to machinery level 4 and as long as you have machinery level 3 you can open the main door at the end of the tomb.
There is a bunch of chests in here that require machinery level 4 that all give 500 exp for opening them. This will get you about halfway to level 5. For the remaining exp I don’t have any good guide for it but you can get the remainder by going back through areas you already cleared and cracking open the chests there.
However, I knew that I was going to try for machinery level 5 for this playthrough before doing it so whenever I saw I could use machinery to crack open a chest even if I had the key to open the chest I would leave it. This is because you only get machinery exp if you open it by using the machinery skill.
Machinery to level 5 from 4 is super easy. Just go to all the jails and open the doors.