I don't know enough about you and your particular problems to recommend GM's. IMO, for everone who finds GM's to be helpful to their deadlifts there are plenty more who will end up hurting themselves or who simply need to deadlfit to be good at deadlifting. As Ross said, GM's will not fix your deadlift technique.
I assume from what you said that although this isn't the first time you've done deadlifts this is the first time you've progressed on them consistently for a longish period of time. Everyone is different and for some going into a fairly aggressive way of loading via this 5x5 may be too much too soon owing to lack of foundation in form, perhaps a weak core (meaning the back taking more than it's share of the work) or any number of things.
Any bad habits or imbalances have a tendency to get worse and get locked in so that you have that much more trouble getting away from them in the future plus the tendency for things to come to a head and develop these strains or what have you. Every lifter is different and statements like this (cookie cutter) is a very good way for any wide range of lifters is really not a responsible statement. If you've gotten a strain or whatever don't assume that the program is smarter than you
I would look at your flexibility. Especially the hip flexors, hams, lower back. Take a bread from the deads for a few weeks and then if possible do what Ross suggested and post a deadlift video using ligher weight with your "best" form so that you can get more opinions.
Also, I noticed the comment about not feeling it in your hams. A good conventinal deadlift, which imo is not the lever method where it's all lower back, should be "felt" in the glutesand hams as much as the back, if not more. In other words you should feel the tension and engagement of those muscles. Not that they should hurt
. So if you don't feel it their that is a place to start.
I would also suggest you think about core strength and frontal plane stabibility. The job of keeping your torso stable should be shared by the entire core musculature, not just the lower back. So if you abs are not "turning on" and doing their job the lower back has to take on more than it should. A bunch of crunches is not the answer to that. Heavy bar rollouts, bridges, front plate squats, basically "stability" exercises is how to get them firing.
The other thing that may be a problem, and that the 'trainers' in your gym may not really see, is that the lift is finshed at the hips, not by back flexion. So make sure that you thrust the hips forward (which is mostly glutes) to lock it out. This can be hard to recognize distinction, the difference between hip and back flexion and it is a frequent problem.
If you find problems then you may need to back off the weight and focus on laying down a foundation for future progress which may involve adding reps or sets or whatever before adding weight. Or if form is really a problem to focus on many very low rep sets with submaximal (relatively) weights for a while in order to focus on 'quality'.