The report comes on top of strong results in April. With solid travel demand and stable fuel prices, Delta and rivals American and Southwest have seen profits rise in 2014, although United is still losing money.
Shares of Atlanta-based Delta rose 11 cents to $40.88 in midday trading. Earlier in the session, they hit a 52-week high of 41.39.
The airline said that passenger revenue for each seat flown one mile rose 7 percent over May 2013. That is a closely watched figure in the airline industry, and it rises when airlines fill more seats or sell them at higher average fares.
Delta said that traffic rose 5.8 percent as passengers flew 17.73 billion miles last month, including flights on Delta Connection. Domestic travel increased 6.8 percent, while international traffic grew 4.2 percent.
The company increased passenger-carrying capacity by 3.6 percent, with many of the additional seats on flights to and from Latin America.
With traffic rising faster than capacity, the average flight was more full — 86.5 percent, up from 84.8 percent a year earlier.
Copyright 2014 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.