While many were expecting inflation to ease up in May, the economy had other plans. 

The consumer price index increased 1 percent month-over-month in May, compared to a 0.3 percent increase in April. Inflation was up 8.6 percent year-over-year, which is up from 8.3 percent last month, hitting a new 40-year high. 

The gains were broad-based, with food, shelter and energy leading the pack, but sizable upticks in the price of gasoline and fuel oil were the obvious culprits behind this month's hotter-than-expected report. 

"Today's CPI report was a doozy," said Tom Graff, head of investments at Facet Wealth, in an email. "While we knew the headline number would probably come in high due to food and energy prices, consensus was that the month-over-month Core CPI would slow sequentially. Unfortunately that didn't happen."

Core CPI, which is all items minus volatile food and energy costs, was up 6 percent, which is the same as last month — dampening hopes of more moderation. 

After spiking in March, energy prices actually fell in April, which gave them even more room to show considerable gains this month.

Gasoline prices were up 4.1 percent in May after dropping 6.1 percent in April, and fuel oil prices were up a whopping 16.9 percent this month, compared to 2.7 percent last month. However, this is still lower than the 22.3 percent jump in saw in March before slowing in April.  

For the year,  gasoline prices were up nearly 50 percent, and fuel oil prices were up an eye-watering 106.7 percent, the biggest year-over-year gain in the history of the report, which dates back to 1935. 

For those watching energy markets, the reading might not come as a surprise. The war in Ukraine continues to rock oil and gas markets, while the broader energy market is bracing for shortages going into what many experts expect to be a sweltering summer. 

Electricity prices were up 1.3 percent overall, compared to 0.7 percent last month, and more gains could be coming down the pike. The Federal Energy Regulatory Commission predicts that prices could increase 233 percent over last summer based on futures contracts. 

Shelter ticked up 0.6 percent, compared to 0.5 percent last month — a small gain that nonetheless fueled the headline number due to shelter's heavy weighting in the index. 

The slight increase comes as the mortgage rates hit 5.23 percent this week, compared to under 3 percent a year ago, and mortgage applications dropped 6.5 percent from a week ago, according to the Mortgage Bankers Association. 

The higher rates and softening demand for mortgages suggest the red-hot housing market could be cooling in response to Federal Reserve rate hikes, but it will take time to see those numbers in the consumer price index. 

In addition, the shelter component in the CPI includes rent costs, which are skyrocketing in many cities across the country, and could see further gains as prospective homebuyers call it quits. For now, both rent and "owners' equivalent rent" (a stand-in for homeowners costs) remained relatively steady. 

Food prices were up 1.2 percent, compared to 0.9 percent last month. In a number of subcategories, such as meat, cereal, and bakery products, price gains slowed, while dairy products were up 2.9 percent, compared to 2.5 percent last month. 

Dairy farmers, notably, are downstream from a number of other cost increases, from record-high prices for fertilizer, fuel, and animal feed. 

Overall, food prices are facing pressure from abysmal wheat yields in the U.S., and the cut-off of crucial supplies from Ukraine, a major exporter of wheat. 

Meanwhile, those notoriously unavailable used cars jumped in price, rising 1.8 percent after dropping in both April and March. This tracks with recent industry data, and the fact that new vehicle supply remains tight due to supply chain-related production cuts.  

All of this adds up to a higher cost of living for U.S. consumers, and a drop in what the Bureau of Labor Statistics calls "real earnings," or earnings after accounting for inflation. 

The latest numbers show a 0.6 percent decrease in May. Real earnings fell just 0.1 percent last month, but were down 0.7 and 0.6 percent in March and February respectively. 

Yet some economists are still convinced that inflation is near its peak, and could soon start sliding back down. 

"We still think it is very likely that inflation is at or near peak," said Graff. "The question is more how long it will stay this high, which really is a matter of how responsive consumer spending will be to tighter monetary policy." 

The report has also squashed the hope for some that the Fed might ease up on rate hikes at its meeting next week. 

"Any hopes that the Fed can ease up on the pace of rate hikes after the June and July meetings now seems to be a longshot," said Greg McBride, an analyst for Bankrate. "Inflation continues to rear its ugly head and hopes for improvement have been dashed again.”