There is a trick where if you have armor that gives extra health, take damage less than or equal to the extra health given, then take it off and put it back on again, you'll instantly regain all of that health. (If done too fast, it won't work.) Since the dps for Trial 5 is 50 (and the previous are less), a single Growth IV/V armor piece (obtainable via auction) could be enough to complete the first 5 trials.

With this, a potential strategy could be the following:

1. Wait for a cheap helmet with Growth IV to be near ending on auction.
2. Grind up quick money (similar to Obtain Coins), then bid on said auction.
3. Sometime during this, mine a few pieces of wood to obtain Foraging I.
4. Collect the auction, equip the armor, and go to The Park.
5. Swim up the waterfall to reach the Trials of Fire.
6. With rhythm after each hit, click on the armor piece twice.
7. After the trial, click on Ryan with the Campfire Badge. 8 ) Repeat steps 6 & 7 for the next 4 trials.

And with that, Trial of Fire 5 is complete!

Video explaining strategy:

Cool Thanks for help!