By Lucia Mutikani WASHINGTON (Reuters) – U.S. single-family homebuilding and permits tumbled in March as soaring mortgage rates increased costs, but residential construction remains underpinned by a severe shortage of houses. The report from the Commerce Department on Tuesday also showed a record backlog of homes approved for construction, but yet to be started. It followed on the heels of news on Monday that sentiment among single-family homebuilders dropped to a seven-month low in April. The 30-year fixed mortgage rate has risen to 5% for the first time in over a decade as the Federal Reserv…