It's too hard to say what happened according to your description. The 5 minute thing might just be that the thin coat of solder on the tip oxidized, and therefore can't be wetted anymore with solder. That's normal, and the fix is normal tip maintenance.
The part about the iron melting itself makes no sense. Irons simply don't have enough power to melt themselves. One exception might be if this is a 115 V iron you somehow managed to plug into 230 V.
Get a real soldering iron, not something with questionable heritage you bought on price from the other end of the internet. Irons without temperature control just aren't worth whatever little you might pay for them. Not only do such irons overheat their tips, which causes them to wear out quickly, but they are terrible to learn good soldering with because the tip is always a mess. Then there is the issue of grossly over-heating sensitive parts.
Big clunky fixed-power 25 W soldering irons with four-facet pyramid tips were OK for soldering wires and resistor leads to tube socket eyelets back in the Pleistocene, but are of little value today.
Anything that is truly temperature-controlled (not fixed or with a "power" knob) is probably good enough for hobby uses. Check out the Weller WES51. Last I looked around, that was the cheapest soldering iron actually worth owning. They can be had here in the US for around $110. Look around.