The F/A-18 doesn't have any of the F-5 left. It's really a completely new bird. It was designed to be a jack of all trades and it's pretty damned good at it. And if you think it can't dog fight, it would be a fools bet. The difference is, the F-18 slows down and uses it's wing loading to it's advantage. It like rough terrain, low to the ground and tries to force the fight there. Unlike the F-14 and the F-15 that fights at either just under of over Mach and goes for altitude.
Actually, as the name suggests the F-18 was designed purely as an air superiority fighter. Like in the F-15 the multi-role came much later. It is air attack, which can also do ground support. And that air attack capability will always show in it's capabilities compared to other aircraft.
Which is in contradiction to a pure "Attack" aircraft, like the AV8B or A-10. Those aircraft would never be good air to air fighters, that is simply not their design.
And I for one never try to compare Naval aircraft with ground based ones. A superb sea launch aircraft will almost always be inferior to that which is ground based, simply because of the compromises that must be made to launch and land them from carriers.
This is the kind of thing that far to many simply overlook when trying to compare different aircraft. They try to treat them as if they were all the same, and they are not. And it has not helped that even the Air Force and the rest of the DoD have confused issues by making a guide for naming aircraft, then for various reasons simply ignoring that convention (like the previously mentioned F-117).
And this happened many times. The A-5 Vigilante was designed as a heavy Naval bomber, and should have been the B-5. I think a lot of the designation naming of the F-35 is because of the Air Force. They tend to be more resistant to adding "A" to an aircraft than the Navy and Marines, and they were the hardest sell because they needed their A version far less than the Marines needed their "B" and "C" versions.
From what I have read and heard, the main proponent for the F-35 was the Marines, which needed a newer aircraft to replace the antiquated Harrier. Then the Navy, which wanted to have at least one stealth aircraft. I believe the Air Force was really only brought in because they could buy enough to make the program functional.
And what resulted was about what was expected with a single basic design for 3 different services. Each had their own requirements and needs, but the Marines got the closest to what they really wanted. And for the first time since WWII finally got a first rate aircraft designed specifically for them, not something bought from somewhere else, or handed off to them because nobody else wanted it.
Even the F-18 started that way. It was a compromise aircraft that the Navy never really wanted. They wanted more of the new F_14 Tomcats, but they were expensive and high in maintenance. The Air Force suggested making a navalized variant of the F-15, but it was too heavy and after conversion cost almost as much as the F-14. So the F-18 was a cheaper aircraft, and early on used primarily by Marine fliers as a replacement for their aging A-4 and other aircraft.
For those of us old enough to remember the Cold War, the F-18 was never really considered the main fighter of the Navy. That was first and last the Tomcat. Even movies like Top Gun could almost be called "Aviation Porn" for the fans of that fighter. Whenever they sent aircraft out for risky missions like against Libya, it was the Tomcat and not the Hornet that did it.
It was only after many improvements and upgrades that the Navy really fell in love with it, and it became what we all know of today. Based on a rejected design originally made for the Air Force.