On the A310 it is actually. Well, not when she’s all fueled up to make the whole 5000 miles, but when prepped for a short/medium haul, the aircraft will certainly push around 4000 feet per minute upto a height of about 12,000 feet, give or take. I 've seen it pass 20,000 will still 2,500 of vertical speed and it has a reason too.
Note how the A310 was one of the first aircraft to receive ETOPS certification (Extended-range Twin-engine Operational Performance Standards). Before that, all oceanic transit aircraft would have four or three engines. In fact that’s how the DC10 and MD11 got their silly tale engines as they wanted to cut down from four but weren’t allowed yet to cross oceans with only two engines.
So the A300 and the A310 where amongst the first to go ETOPS and they weren’t quite experienced with it yet. So they just fitted these aircraft with HUMONGOUS engines that were well able to provide sufficient power with only one running. They then needed a big tail rudder to compensate for. And this is why Airbus later on experimented with the A330 doing two big engines, and the A340 (which is the same aiframe design) with four small engines, getting the smaller tale as she would suffer less asymmetric thrust when losing an engine in flight. Well, losing thrust of course, not the entire engine. You should definitely not lose an entire engine during flight. That’s just wrong.
So, back to the A310. Small aircraft, big engine. As they were new to the whole concept they didn’t take any chances and just fitted her with these two beasts. When they work together, they’ll sure produce you that 5000 feet per minute. It’s only later as they grew more accustomed to it and engine technology developed that engine performance was more sane again.
Also. Please not that you should select the engine thrust settings (next to the gear lever) to either flex or auto. (It will go to auto after flex takeoff). Don’t have them run at TOGA all the way up to cruise. If you’re gonna to not bother with flex settings, adjust for climb performance manually on that same panel. It will still provide you with a good 4000 feet a minute below 10K when in climb mode though.