My marketing expertise may be lost on some...and marketing is exactly what this is. The old mantra "gotta spend money to make money" is an absolute truth.
As an example, if $300k is spent printing and mailing these letters to every member (assuming it is an even 5 million), that's 17 cents per member, which isn't that much considering that they do get bulk mailing rates, 17 cents is certainly realistic. If 30% of the membership responds with a $5 donation, that's a $7.2million dollar profit.
In reality, the numbers may vary but I am using the textbook figures of a successful marketing campaign. Depending on economic and geopolitical issues, results can vary. Lately, the NRA has had an increase in membership, suggesting that a ramped up donation drive could be very successfully conducted. Considering that those who join are highly motivated and patriotic, I believe the NRA has a very high return rate regardless of political swings. 30% is a textbook ideal, but with donations averaging $5 per response, you would only need only 1.2% return to break even and 4% return to be a success.