A couple of weeks later, I have decided to tell you how I did it. It's been over a month since the transfer.
The other two answer were good, but they couldn't simply work in my case. Since the larger tank was over 5 time bigger keeping old water wasn't really an option. You need movement in the water so it don't become stagnant, especially over a 2 weeks period. Also since I wasn't just moving the fish from one tank to the other, it was harder to fill up the 75gal with tank water. They were in 2 different apartment witch made keeping water impractical.
Don't get me wrong, if it's practical to dump old tank water in the larger tank to fill it up partially at least, go a head and do it. But if you are in a situation like me, where it is not practical, filling with tap water is correct. Since most of the good bacteria live in the filter and on other solid object (substrate, decoration, plants, etc) by transferring the filter, I had transferred the most of the bacteria.
Here how I did the move. I had 20-40 red cherry shrimp and ~10 neon tetra, 4 danios zebra and 2 endler. I first removed most of the decoration from the tank. This was mostly plants, a couple of rocks and some wood. Then I started to drain the tank. I took the filter media and dropped them in a large ziplock filled with old tank water. Than I filled a plastic container with about 2-3 gallon of water, the rest went to the sink. When the tank was under 25% water left, I started to catch fish with a net. I put them in the plastic bin for transportation. It's the same bin I dropped 2-3 gal of old water in it. When I had all the fish in the bin, I started to catch shrimps. Those I put them in a small bottle filled at 50% with tank water. When every one were in their transport container, I took off. The first thing I did at my new home was to drop the containers in the new tank just like I would have done if I had purchased the fish. While the water were matching temperature, I reinstalled my filter on the new tank. After about 20 min, I started to add water from the new tank in the container. I repeated the above step a couple of time and after that, I scooped the fish out of the container and put them in their new home. For the shrimp I removed the cap and let the bottle sink in the tank (I didn't mind ~500ml of old water in 75gal).
A couple of day before the move, I started to feed less. About 25% less by feeding and the two day before the move I didn't feed. When they were moved, I didn't feed the same day. But the next day I feed them lightly.
It's been over a month since the move and I didn't lost any fish. They are all going great. For the shrimp I can't say because it's too hard but I still see plenty so at least a large portion survived.