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How do people ever figure this stuff out?
The same way that people figure out where mediaeval European coins are from, or modern Islamic coins: they read the writing on the coin, and compare it to known historical records to see if such a king from such a place is known to exist.
Just because the writing is difficult for you or I (or even a modern Arabic-speaker) to interpret, does not mean it is untranslatable.
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Are the exact date and mint location written on this somewhere, or is it just a general type?
The Muslims were early pioneers of routinely putting the date and mintmark on coins - though to be fair they copied the concept from the Sassanian Persians after they'd conquered them. The standard formula is a sentence which reads something like "This dirham was struck in Baghdad in the year five and twenty and three hundred". However, as time went on, the date and mint-name often got pushed to the outer extremities of the coin, where they are often either worn (or clipped) away, poorly struck or missing off the flan altogether. On your coin, as stated in the example echizento linked to, are on the obverse, which is the left pic on your coin. I'm not sure there's enough of the obverse outer legend on your coin to read anything meaningful.
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Can a 700-year-old silver coin really be worth less than $5? Have I just been missing out?
If it's common enough, yes. And there are currently 106 examples of this basic coin type (in both the dirham and double-dirham versions) over on
the zeno.ru pages.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis