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If the company checks out as legitimate then I would be inclined to do business.
You can fax or phone your credit card details to the most legitimate business on the planet. That doesn't mean that, on any given day, someone in that company won't commit a wrong.
It tells me that it wasn't worth that price in the first place.
This is one of the most basic tricks in sales, it makes you think you are getting a real good deal.
For me to spend £5000 on a domain name, it would have to be a good 3 letter .com or a nice one word .com, probably with traffic also.
Even £700 is a lot, unless it's something you have looked seriously into and nothing else will do.
Have you looked into different extensions?
Be careful faxing your credit card details to anyone you don't know. For that amount I would use Escrow.
I offer congratulations to you for not overpaying for a domain. Use still possess your $700, as you elected to not apply it on what may very well have been a poor purchase decision. Use it wisely.
In the future, when you read about someone selling their mid four figure domains for less than 400, remember this moment, and do your level best to resist the urge to overpay once again. After all, paying even $40 for an $8 domain is not a bargain if all you get in the end is a mediocre domain and the false pride of not having paid $800 :)
of course, this is safe.
you can reverse the transaction if you don't get the domain name.
i don't know what the issue is.
as for those who are going on about price/value in this thread ... that wasn't the question and is not relevant as to if faxing your credit card details is safe or a good way to complete the deal.
someone was interested in buying a domain name off them for $4000+ and after a few weeks and emails he got them down to $150 WOW.
Only "wow" if the domain was worth something more than $150. Not all that many are, but if even a fraction of people pay something nearer a ridiculous asking price, that's "wow" for the seller.