It has 3 legs on the back and two on the front. The top is solid wood. It wobbles both from front to back and side to side (front to back is worse). What can I do to minimize the wobble knowing that I have limited tools and experience in wood working? I want to make the table sturdy by itself, so I don't want to screw it to the wall. A solution with readily available materials and beginner friendly would be ideal. I enjoy solving problems like these, but I think in this case I lack the knowledge to figure out a good solution. Extra points for creative thinking.
Your table and legs and floor are turning into parallelograms. This is because the legs have no resistance against swinging on their mounts.
I suspect that these legs are not designed to prevent this, because they expect the desk surface will be anchored in both dimensions by something else, e.g. Being attached to a wall.
You will either need to select different legs, or find a way to brace these. This is why most desks and chairs have some sort of cross bracing between legs, but you need more than that, or you'll just have more parallelograms.
If it were me, I would use steel angled shelf brackets that have a nice triangle shape to them, and drill and tap appropriate machine screws into the legs, using the steel in the legs to hold the screws. I would not drill through the hollow legs and use a bolt and nut, because all that would do is squash the hollow leg. You would need to learn the fine art of using a hand tap, and it would also help to get centerpunches to get the pilot holes in the right place, but that is not excessively hard. Just tedious.
Since the table is wide and not very thick, even were you to correct the issue now, it likely would warp a bit over time -- specifically, the middle of the side with two legs will sink slightly. Therefore, any remedy should be adjustable to compensate for that sag.
You could buy and install adjustable furniture levelers, or you could devise your own, depending on the design of the legs... or, for the three back legs, which are out of the way, insert thin siding shingles or similar inclined planes, which can be pushed in as needed (nothing would be needed for the front legs, if you don't mind a slight slant towards the front).