As Doc says, this is almost certainly not going to matter. The ESTA will continue to be valid for future visits, and the future visits can be transit or not transit, irrespective of the reason for your first visit.
For future reference though, a visit is for transit:
for persons traveling in immediate and continuous transit through the United States en route to another country, with few exceptions. Immediate and continuous transit is defined as a reasonably expeditious departure of the traveler in the normal course of travel as the elements permit and assumes a prearranged itinerary without any unreasonable layover privileges.
Entering and exiting by land are not excluded, and there is no actual time limit as long as you are taking an "expeditious" (meaning as short as practical) route to the other country. Arriving at LAX and driving immediately to Tijuana in order to cross to Mexico certainly counts. However that does assume you drive expeditiously to Mexico, that you don't hang around for a couple of days to do sightseeing. The several hours you will spend in the US doing this are certainly within the limits of the definition of "transit". Airport layovers can sometimes involve staying a couple of days, and are still considered transit.
The issue of transiting through the US and then transiting back again five weeks later will not be a problem. When your friend re-enters the US after five weeks they do so on the same entry permission they had before, and will thus be expected to leave within 90 days of their original entry. As long as your exit from the US to Mexico and your re-entry from Mexico are recorded by US immigration then it does not "look like you spent five weeks in the US" and US immigration will not think that.
The correct answer is Yes, but it probably isn't going to make a difference.