To live like a noble(aristocrat) is at a minimum, 10g per day for food, clothing, etc. 10g per day for maintenance of your noble estate. 600g per month and includes nothing extra. No parties. No hosting contests. Nothing. 600g per month at a bare minimum. Going with 10,000(I've never seen anyone get even that much by level 5), you have about 17 months of money.
Page 133 of the *DMG* tells us how many treasure hoards a party is expected to find over the course of a typical campaign. If we make a few assumptions, we can use this information to estimate how much wealth a character has accumulated at each level of his career. My assumptions going into...
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IF the DM allows it. And IF the PC can find or come up with the correct formula. And IF the PC can find the components needed. And IF the PC spends 4 days and 100g(DMG page 129) on the potion, he can sell it for 25-50gp(50-100gp x 1/2 for consumable - DMG page 135) IF he can even readily find a buyer. A minor permanent item might get you 100g if you get lucky. You need to have an exceedingly generous DM in order to make a decent living.
Better to just go adventuring.