I always reach fishing level 5 on the fourth day easily using the strategy I'm about to tell you:
On the SECOND day, I take Willy's fishing rod and go straight to the mountains, where I place my chest in the lower corner of the map, where Sebastian smoked every day. There, I weigh non-stop until midnight, then I go back home and sell all the fish. (Trust me, you'll understand!) Always end the day with fishing level 2...
On the THIRD day, I take advantage of the rain and go to the beach, where I weigh eels and snails. If you didn't get 2000g of fish on the second day, fish on the beach until 4 PM and then go to Willy's house and sell the fish you caught, buy the fiberglass rod and use the rest for bait.
Q: But why do you do that?
A: Getting the fiberglass fishing rod quickly makes you fish faster > more fish > more chests > more experience > more money!
So, with the fishing rod in hand, I fish until 1:50 AM, store all the fish in the beach chest, and pass out. That way, I reach fishing level 4!
On the fourth day, I return to the mountains and fish in the same spot until 2 AM, when I pass out with all my fish, thus reaching fishing level 5! Then, I go to Willy with the fish and sell everything on the fifth day.
Following this strategy, I sell everything at once because the fish from the mountains go straight to my inventory, and the fish from the beach stay there waiting for me to sell the first batch and collect them. Besides reaching fishing level 5, I usually get 7,000 to 10,000 gold with this strategy on the fifth day! You decide if you want to hurry up and get the mine, spend the day planting seeds, fish a little more... Anyway, I hope this helped!