Student pilot reported they entered the traffic pattern at the wrong airport on a solo flight and descended to an unsafe altitude. ATC provided instructions for student to fly to their destination airport where student landed safely.

Narrative

I am a student pilot with over 76.5 hours of total flying over the past one year and I am trying to finish my private pilot license training my meeting the PPL check right requirements.On Day 0; it was my first long cross country solo flight; and I had planned flight starting at Addison Airport (ADS) to ZZZ1; followed by a flight from ZZZ1 to ZZZ2 and finally from ZZZ2 to ADS.I got my weather brief by calling the 1-800-weather-brief at XA:00 in the morning and there were no weather advisories/NOTAMS applicable.I met with my flight instructor preflight and showed him my NavLogs and he was satisfied with them. I took off around XE:30 PM and successfully reached ZZZ1 using pilotage and dead reckoning and landed there without any issues. I utilized VFR flight following and explain to them that I am a student pilot on my first solo XC flight. I resumed my flight to from ZZZ1 to ZZZ2. I called the ZZZ center and explained to them that I am a student pilot on my first cross-country flight and requested flight following that was approved. I reached ZZZ2 and landed there successfully and re-fueled the aircraft.Then; I took off from ZZZ2 again picking up flight following and flew towards Addison. This flight was about 40 minutes long and at planned cruise altitude 4500 feet. Just before ZZZZZ [one of the way points]; I was asked to Descend to 3500 feet; which I complied with and continued to fly on the course as per my NAV log. I was handed over to the tower and as I was approaching ADS; I introduced myself as a student pilot on my first cross country and asked for vectors. ATC asked me to continue on the current course and later asked me to make a 20° right which I did. He asked me to continue on that course straight to runway 16. At around six nautical miles; he asked me if I see the airport at 11 o'clock. I looked at at 11 o'clock and I thought I identified an airport which eventually ended being a highway in the distance. A few minutes later; he asked me again if I have the airport insight and that I might be looking at DFW airport. At that time; I was less than 5 miles as per GPS and I did not think I was looking at the DFW airport but realized that I did have trouble locating Addison Airport. I looked at my ForeFlight map on my ipad and I was headed in the right direction so I kept going and kept looking for the ADS. At that time; he asked me again if I see the airport around 11 o'clock and this time I saw what I thought was a Addison in Airport; which later turned out to be Dallas air park. It did not occur to me at that moment that this could be Dallas air park which I have seen before after I took off from Addison airport. It has similar runway 16-34. I tried to turn left and go straight in to the runway 16 but overshot the airport. Then; I announced that I overshot the airport and told him that I'm going to turn around and enter left downwind. At this time he reminded me that I was low; but that was because I was setting up for landing at Dallas air park which I believed was ADS. When I was in the left downwind; he reminded me that I am not at Addison Airport and at this time I realized that I was at the wrong Airport. ATC asked me to climb which I did; and at that time he asked me to look for a meridian; which is flying straight in to Addison runway 16 and follow him. I promptly located the traffic; and I followed him. I could now clearly see Addison Airport and I flew a stabilized approach and landed uneventfully.The probable cause of me ending up the wrong airport was due to the difficulty I had identifying Addison Airport given the urban location. Due to my job; most of my training occurs later in the afternoon and we fly back to Addison in the dark and usually my instructor takes over the final approach and landing. Identifying Addison Airport has always been a challenge for me although It has gotten better over time.During the Post flight briefing we talked about various landmarks that help identify the airport. On our next few flights; we will be flying multiple approaches and identify visible landmarks around the airport for a stabilized approach. Also; my instructor will be training me in ILS programming to localize the airport in the next few flights.