How are Elizabeth I and Catherine of Valois (Henry V's wife) related?
Elizabeth I of England was the great-great-granddaughter of Catherine of Valois.
Catherine of Valois was married to Henry V as you say. With him, she had a son who reigned as Henry VI. Some years after Henry died, Catherine married Owen Tudor. With Owen, she had a son named Edmund Tudor. Edmund Tudor married Margaret Beaufort, whose great-great-grandfather was Edward III of England. Edmund Tudor and Margaret Beaufort had a son who reigned as Henry VII. Henry VII, of course, was the father of Henry VIII and Henry VIII was, quite famously, married to Anne Boleyn. From their marriage came Elizabeth I.