WASHINGTON—U.S. home prices soared in April at the fastest pace since 2005 as potential buyers bid up prices on a limited supply of available properties. The S&P CoreLogic Case-Shiller 20-city home price index, released Tuesday, jumped nearly 15 percent in April from the previous year. That is up from a 13.4 percent annual gain in March. Many Americans have sought more living space since the pandemic began, seeking larger homes in suburbs rather than apartments or smaller homes in cities. Historically low mortgage rates, restrained in part by the Federal Reserve’s low-interest-rate policies, have also spurred demand, just as the large millennial generation ages into a peak home-buying period. The price gains have been so dramatic that home sales have started to slow as more would-be buyers are priced out of the market. Still, economists said there is little sign that the housing market’s blistering price increases are likely to …