Given that you "forgot" $3,000 per year, which is an increase of more than 50%, I would do nothing until you actually track your expenses and practice living in your target amount. Set up a separate account. Spend money *only* from that account. Every single penny you spend needs to come out of that account. Transfer in $10,000 over the course of a year. Make sure you transfer out the interest. You want only $10k to be available in that account over the course of a full year. Also, make sure expenses that don't occur every year are included, like a reasonable amount for home maintenance, car repair/replacement (if you have a car), perhaps things like emergency travel to visit aging family, etc. Your life is going to change a lot in the next 4-5 decades.
Can you do it comfortably? If so they that makes a reasonable FIRE goal for you. As others have pointed out "FIRE" doesn't mean you have to stop working and earning. It just means you don't have to worry about those things. If you are laid off, you shrug indifferently. If you grow to hate your job, you quit without worry, and take your time finding something else.
Also, you say you'll "always" be able to work and make $5k. What about when you are old? What about when the economy is abysmal? If that $5k is simply your fun money, those scenarios are no big deal. But with such a tight budget, you are going to actually *need* that $5k, which to me would force me to be much more conservative.
I'd likely work until the house was paid off and I had enough to give me nearly the full $10,000 (assuming your test reveals that to be a truly accurate number, about which I'm doubtful). So I'd probably get to at least $200k, and the commit to trying to bring in $10k per year, rather than $5k, until I was at $250k. After that I'd let my expected $5k/y income be that fun money, plus a hedge against unforeseen changes in life. I wouldn't be comfortable committing to such a very tight budget for such a very long time, given that life is unpredictable.
If you have side projects you want to start now, do it. To me it would be worth it to work an extra 6 months if it meant 3 years of doing something that truly interested me. If it is going to take you 4 years to pay the house and then another 5 (wild guess) to save up your $250k), rather than wait a decade, start one of those side projects now and work an extra 6 months. Wouldn't it be worth it?
Also, if your timeline is too long, consider ways to increase your income now.