Yes, this happens. Yes, you should be able to keep the same class of service. You have options, although we probably need more information.
- Is this a ticket you booked on United miles?
- Are the flights all on United planes, or are they on one of United's partners? If it's on a partner, the United agent might not be able to select seats, but they should be able to give you a record locator for the partner airline, and you should be able to call that airline and select seats.
The five-hour change is significant and should allow you to make changes to your reservation without a penalty, even if the options are currently listed as costing more United miles than your initial reservation.
If the flight is purchased with United miles and United (or one of their subsidiaries) flies the entire way to your destination, you should be able to change the reservation to one that fits your desired times, regardless of the cost. If you're flying, say, from Cleveland to Stockholm, you should be able to change to a CLE-EWR-ARN that fits your desired time without triggering any increase in price. If you get push back on this from a United agent, you'll need to hang up and call back, but you should eventually find an agent who fixes this.
If the flight is purchased with United miles and United does not go all the way to your destination on their own planes, you have flexibility, but it might be trickier. For example, if you were flying to a small town in Germany, you might be flying United to Frankfurt and then Lufthansa from Frankfurt to that town. United can't open up availability for that final Lufthansa flight, but they can get you to Frankfurt on your desired schedule on United flights.
If you can give us more details, we can do more to assist. Either way, you shouldn't be downgraded because of this change.