I used the Texas Method for about 3 years and really enjoyed the program and seen good results over the years.
I believe the typical set up, or at least the one written in the article you mention, has you finding your new 5RM (1 set of 5 reps heavier than last time). You may (will) require several sets to ramp up to a new 5RM set. So rest assured you are still getting in some quality work that day but it does feel too easy some days. Remember it’s about triggering a response for the body to grow stronger and not about how tired you can make yourself in a workout. The reason for the Rep Max to begin with is to make your body say “wow, that was terrible! I don’t want to do that again; I need to be better prepared next time.”
Later on if you start to find you can’t ever reach a new 5RM it could mean you are starting to get to a point where you won’t see dramatic progress in just one week of training. The best first course of action is to Deload 10% while making an extra point to eat more good food, drink more water, and sleep more. If that doesn’t work you can eventually reduce it to a 3RM on Fridays to keep moving the strength needle forward for a bit longer. I would switch to a different program after exhausting the 3RM gains as I don’t see any value in doing doubles or singles each week as new PR attempts. You will likely just drive yourself into the ground doing that.
If you read about the history/legend for how this program came into existence you may discover the story about how Glen Pendlay made a deal/bet with his athletes that if they could post a new 5RM on Friday they could cut their workouts short and didn’t have to do a full 5x5 session that day.
I used to use a similar motivation in my training where if I didn’t hit a new 5RM I would have to do 1-2 heavy back off sets. It motivates you in that moment not to give up and grind through to a new 5RM …if possible. Or suffer failure and think about it the entire time you are doing back off sets about how much you suck.
A final word of advice for you while using the Texas Method; Friday is the important day and not Monday or Wednesday. Hitting a new 5RM is all that really matters; even if it means pulling back on load for Monday’s 5x5 session. You could even try a slightly different rep scheme like 6x4 or even 6x3. This could be just a small enough change to make all the difference to continue progressing.
I always had my best progress BECAUSE of the work done on Monday. However, you can (will) get to a point where a hard, new 5x5 max on Monday kills your progress for the remainder of the week. If this starts to happen I suggest pulling back on load (weight on bar) on Monday and see if you can still continue driving up your 5RM on Friday. Doing a 5x5 weight you already did previously for a few weeks in a row can still build strength so don’t get confused about Monday having to be a new 5x5 max just to make progress as this will eventually stop you altogether.
Good luck. It’s a great program and I hope you also find lots of improvement in yourself with it.