Only being able to hold 5 planks of wood to repair damage to ships is a bit annoying. Same for various other supplies that make larger exploration difficult. I have spoken to people around the outpost and I couldn’t find anyone who would allow me to increase my inventory size, is it possible?
No, inventory size is fixed in this game. You can’t purchase upgrades at the moment at least.
It might seem annoying at first, but it is intentional and for a good reason. Since you could be out at sea and come across a team of players who have put 100s of hours into the game, they would ruin you in seconds since they have more items and health etc. At least with this, the only difference is experience. If you get killed, it is because the other person is better than you and not because they had the upper hand with all of the upgrades they have.