The Russian law #844 (7 August 2001) by the Russian Ministry of Culture governs the rules of importing / exporting cultural values from Russia.
It says that it's only forbidden to take out from Russia cultural items that are more than 100 years old. There is also another clause that says that you need to obtain a special permission if the item is between 100 and 50 years old. Additionally the law says that cultural works that are visual in nature are excluded from this regulation.
However, there's also another law - N 4804-I "About the order of exporting cultural value items from Russia" – it actually lists icons as the items that can only be brought out of Russia with a special permission obtained from the Russian Ministry of Culture.
The both laws say that if the item is modern or is a souvenir it's not governed by that law. So basically it means that if you buy a new icon at a market or in a shop and can produce a receipt, you should not have to declare it when you leave Russia.
If your item is more than 50 years old then you definitely need to get a permit to get it out of Russia - contact http://www.mkrf.ru
(some items are exempt from this regulation, however, it's much safer for you to get this permission just to avoid complications at the customs).
Another clause of the law says that if the work belonged to you for 20 years or longer and it's less than 50 years old, you have the right to bring it out.
In your situations the icon is 34 years old, so theoretically your friend was not breaking the law bringing it out of Russia without a permission.
There are 3 options possible in your case (you need to consider them all):
1) The customs is right and that particular icon was protected – in this case they have to produce a proof that this item, which is less than 34 years old, is of the cultural heritage (which is extremely unlikely). It's going to be very difficult for them to do it, so I don't think this case will work out in their favor.
2) The customs is trying to get money from your friend using the fact that she doesn't know the law so well. In this case she should produce the law to them and prove that the icon is less than 50 years old (either by showing a receipt from the shop or through some independent expertise).
In the two cases above it's weird this $5000 sum for closing the case - you should know that bribing in Russia is illegal and your friend and you might get into more trouble if you try to buy your way out of the court this way.
3) It might be that you're a victim of scam. Your friend might have made this whole story up (together with some friends in customs or alone) to get some money from you. Too many parts don't fit and the weirdest part is about $5000 and no jail + keeping the icon or $2500 + give up the icon + no jail – this is too flimsy and just doesn't fit in at all.
References to the law:
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