Edward V was age 12 upon the death of his father, Edward IV. He "reigned" for two and a half months before he was formally deposed (and likely murdered) by his uncle, Richard III. He was never crowned, was a minor, and controlled effectively zero territory, as his uncle Richard had taken control of the country even before Edward's deposal was confirmed by parliament. Despite this, Edward is included in historical lists of English monarchs and his regnal number is recognized by later monarchs.
Arthur, duke of Brittany and earl of Richmond, was age 12 upon the death of his uncle Richard I. Sources differ as to whether Richard preferred his nephew Arthur or brother John as his heir, and Arthur was never crowned, but Arthur had the stronger claim on the tradition of primogeniture. Arthur claimed the throne and -- unlike Edward -- controlled some territory, though not in England, but at least in the broader Angevin empire, and lived to maintain his claim far longer than Edward (around four years) before he was captured (and likely murdered) by his uncle, King John.
Empress Matilda was age 33 upon the death of her father, Henry I. She was his designated heir, had the support of much of the English nobility and, though she was never crowned, she controlled southwestern England and all of Normandy for decades.
How did Edward V come to be recognized as a monarch of England despite never being crowned while both Arthur and Matilda -- neither of whom were crowned, but both of whom controlled significant territory, made strong claims to the throne, and pressed those claims far longer and more seriously than Edward V did -- came to be regarded simply as "claimants?"
There are two main reasons. The first is that Edward V was publicly regarded as king for a month, pretty much universally. Matilda and Arthur's claims were never uncontested. Our habit of remembering our monarchs as big chronological list doesn't really lend itself to the concept there being multiple monarchs at once. Furthermore, while many people at the time saw Matilda or Arthur as the rightful ruler, that's not a concern for historians in this sense. Lots of English monarchs, such as William I or Henry IV, were usurpers in some way.
The second main reason is that Edward V was officially regarded as the lawful king by the Tudor regime. Richard III may have declared Edward V illegitimate in the Titulus Regius, but this was repealed by Henry VII, who ordered that all copies of the document be destroyed. This emphasised that by taking the throne, Henry Tudor had overthrown a usurper. It also ensured that his new wife, Elizabeth of York, was regarded as the legitimate child of Edward IV. Had Richard III won the Battle of Bosworth, Edward V might not have been regarded as an English king.
Sources David Carpenter, The Struggle for Mastery W. L. Warren, King John Dominic Mancini, The Usurpation of Richard III S. B. Chrimes, Henry VII