Did the Smithsonian Museum just offer a $5 'apology discount' to black people as a form of voluntary reparations? No: African-Americans will have to pay the regular admission price, just like everybody else. And since that price is zero already it means they won't have to pay a thing... The story about the discount (in the form of $5 gift cards) is a complete fabrication.
The hoax originated with an article published on March 17, 2018 on satirical website Daily World Update titled "Smithsonian Museums Will Offer $5 'Apology Discounts' To Black People" (archived here) which opened:
The Smithsonian Institute in Washington DC is the 2nd largest museum complex in the world next to The Hermitage in St. Petersburgh. For over 300 years, the Smithsonian has graced our national mall and helped to make DC the exciting tourist town it is today.
Now, on the anniversary of the addition of the African Arts Museum, the non-profit has announced that it will give a "$5 discount" to all people of African-American origin. Since admission to the museum is free, the "voluntary reparation" will be handed out in the form of a gift card good for use at any of the museum's gift shops or cafeterias.
The spokesman for the museum ("Art Tubolls") that is quoted in the story does not exist. His name is an anagram for "Busta Troll", the owner of the website (see below).
The site Daily World Update comes with a clear satire disclaimer at the bottom of each article:
the use of humor, irony, exaggeration, OR ridicule to expose and criticize people's stupidity or vices, particularly in the context of contemporary politics and other topical issues.
If you disagree with the definition of satire or have decided it is synonymous with "comedy," you should really just move along.
The owner and main writer of the site is self-professed liberal troll Christopher Blair, a man from Maine who has made it his full time job to troll gullible conservatives and Trump supporters into liking and sharing his articles. He runs several other websites such as ladiesofliberty.net, shareotonin.com and dailyworldupdate.com. Sometimes he is also known under his nickname "Busta Troll". He has at least one accomplice who writes under the pen names "Freedom", "Captain Jellypants", "Butch Mannington" or "Captain Buck Atlantis".
Articles from Blair's sites frequently get copied by "real" fake news sites who often omit the satire disclaimer and any other hints the stories are fake. Blair has tried to get these sites shut down in the past but new ones keep cropping up and he keeps knocking them down.
If you see one of his stories on a site that does not contain a satire disclaimer, assume it is fake news. If you do see the satire disclaimer it is of course also fake news.