Auto-Train Corp. yesterday revealed plans to sharply curtail its service for five months of the year and to raise its fares by amounts ranging from 13 to 56 percent.

Auto-Train service between Lorton, Va. and Florida will be cut back from seven days a week to five days from May 23 through October 25, except for the mouth of September, when the train will run only four days a week.

The Tuesday and Wednesday trains in both directions will be dropped for the entire five months and the Thursday trains will also be eliminated during September, the company said.

Unlike the temporary schedule reduction, the company plans permanent fare increases. The reductions in frequency of service do not require the approval of the Interstate Commerce Commission, but the ICC must review Auto-Train's request for higher fares.

The railroad said it wants to raise the basic fare for carrying each automobile from $99 to $155, each way, a 55 percent rise. Under the new fare schedule, the charge for each person accompanying a car would decrease from $79 to $70.

But because Auto-Train is authorized by the ICC only to carry passengers and car together, the total fares would still rise. The cost for a car and one person would rise to $225 from $178 a 26 percent increase. If two persons accompanied a car, the fare would rise to $295 from $257, an increase almost 15 percent.

The simultaneous announcement of fare hikes and service cuts apparently indicates a financial crunch is on at Auto-Train, a private publically-traded company that does not receive government subsidies. Most other passenger service is subsidized.

After struggling to make a profit for several years, Auto-Train lost $2.5 million in the eight months ended Dec. 31, 1977. It changed its fiscal year and the company reported profits of $685,000 for the three months ended March 31, a period in which traffic to and from Florida is heavy and the company traditionally makes money.

Phillip Cruver, assistant to Auto-Train president Eugene K. Garfield, said he could not estimate how much money the company would gain from the fare increases or how much it would save from cutting service.

Cruver said the cuts in service would allow the company to operate more efficiently during the months when traffic is low. During these months the train can run close to capacity five days a week rather than run seven days with many empty seats, he said.

Tuesday and Wednesday are the days with the lowest traffic, Cruver added, "so we annulled those days."

Noting that Auto-Train had eliminated Tuesday trains during the summer of 1975, Cruver said the reduction in frequency is not expected to adversely affect use of the trains by travelers.

But others familiar with the company's operations said they considered daily service essential to Auto-Train's success. When the trains do not run every day, potential passengers are confused and ridership falls off, they contended.

Cruver said Auto-Train travelers who make reservations before June 15 will be charged the old fare regardless of when they travel.