Age 65; does this sound right?

If that's manageable for your current fitness level - not over-fatiguing, among other things - yet somewhat challenging to current capabilities, it's fine.

If it's a big jump up from what you've been doing, don't take it on all at once, instead ramp up gradually. The usual recommendations are around a 10% increase per week, at least on the cardio side of things.

Retro and others will give you better detailed advice about strength training than I can, but IMO the "manageably challenging" idea still applies there, too. The 4-6 pound dumbbells might be too light or just right - he's right about the last couple of reps needing to be quite challenging, almost the most you can do while maintaining good form.

However, if it's been a while since you've lifted, I'd endorse starting on the light side, getting good form grooved in, conditioning the connective tissues and being attentive to any muscle imbalances or weakness, before going up. Injury has a higher cost IMO the older I get: Faster detraining, slower rehab and rebuild when resuming.

Overall, when scheduling, remember that recovery is where the magic happens: The body rebuilding better after the stress of exercise. How much recovery, of what type, and when, also depends on one's current individual status and on the specific mix of activities.

I'm 69 and female, have been quite active for 20+ years in various ways. As I've aged, I've found that I need to be smarter about planning in recovery. I'm not saying I necessarily need to do less than when I was younger, but rather that overdoing for current capabilities is more difficult to recover from than when I was younger. With reasonable planning and progression, I can still do . . . whatever.

I'm interpreting "zone cardio" as the so-called "fat-burning zone" idea. If that's not correct, please clarify.

Given that assumption, I think it's important to say - put very, very cautiously, because it's extra dependent on current fitness: In the long run, there's value in including a small amount of quite intense cardio, too, perhaps especially as we age. Minute for minute, it's more fatiguing than lower-intensity cardio, so it's necessary to have good cardiovascular base fitness before taking it on, and it does risk reducing some daily life calorie burn if done too soon or for too long/too often. Dosage really matters. However, it helps some physiological systems that tend not to get useful stress in other ways.

I'd also say that for me, anyway, the eating side of the equation is more important for maintaining a good bodyweight than the exercise side. That's not to deprecate exercise, because it's great for a body - health, mood, more. But I was very active for a dozen years, training pretty hard 6 days most weeks, with good strength for our demographic and good cardiovascular fitness (endurance, resting heart rate, heart rate recovery, competitive performance) . . . while staying overweight to class 1 obese. Getting the eating side where it needed to be was key for me in achieving and sustaining a healthy body weight, where I've been for around 9 years since weight loss. That was easier than I'd anticipated, to my surprise.

Best wishes - the fruits of success are worth the effort required, IME!

Losing weight slowly is fine, especially if not severely overweight, which you aren't. I'm a big believer in the value of a relatively easy plan, compared to "lose weight fast" plans which IMO don't usually end well, but do end quickly. Sometimes some different food choices or food timing can make it more pleasant to stick with lower calories.

For sure, in our demographic, adequate protein spread through the day is really important for health as well as potentially satiety. This explains that, in case you're not familiar:

https://www.jamda.com/article/S1525-8610(13)00326-5/fulltext

The 20 minutes of high intensity sounds fine, if not currently too exhausting - maybe once or at most twice a week IMO once there's enough base fitness that it's not toooooo fatiguing, unless you have a clear reason to do more. At times in the past, I've followed formal training plans for my cardiovascular sport, and the high intensity bits are in small doses and not too frequent, for sure most of the weeks during a training cycle, maybe ramping up a little more for a short time in the lead-up to a competition to sharpen VO2max for the event.

If the weights classes you're taking are those group classes where everyone simultaneously does the same exercises at high repetitions, it's normal for those to use lower weights. I don't know what your specific goals are, but that modality tends to be better for building muscular endurance, not as effective as some other modalities for building either strength or muscle mass. I'm not saying it's bad or wrong: It's not. I'm saying that it aligns with some goals better than with others, and I don't know what your specific goals are. If for you it's more about general health and enjoyment, that may be great.

Soreness isn't really the indication of progress in strength training. Usually, true soreness is about a short period of adaptation to a new exercise stress. After that adaptation, my experience has usually been that the feeling that goes along with strength/muscle progress is more of a pleasant "I've worked out" kind of taut feeling, not really soreness. Maybe others differ.

Retro's comment about being close to but not at failure in the last reps is an indication of reasonable challenge, I agree. I'm not sure how to interpret when you say "the weights feel heavy" - if it's that, that's good, until you get stronger. 😉 It's normal to need higher weight for some exercises than others to achieve that challenge, too. Some of the classes I've seen stick with the same weight throughout, challenging for some exercises but less so for others.

I'll leave it to Retro and others more knowledgeable about strength training to be more specific, but generally doing the same exercises with the same weight/resistance isn't the most effective route to gains: Increasing reps at the same weight might trigger some gains, but there's only so far we can go time-wise with increased reps. The most efficient route to increasing muscle mass or strength will involve progressive increases in weight, generally, though there are some other ways to add useful stress.

Ann's advice about easing into it is spot on.

I wonder though, what you actually mean re the weights workouts.

Because I'm thinking of a typical lifting workout such as, 10-20 reps which are challenging at the end, put weights down and rest 1-2 minutes, repeat. I'd also note that we're all much stronger with certain exercises than others, so e.g. I use at least 8 different dumbbell weights from the lightest for lateral raises and wrist curls, to the heaviest for bench press and one arm bent over row (and heavier with barbell for legs), and in between for curls and Bulgarian split squats. Even if 5 pounds is challenging for you at this time in certain exercises, I seriously doubt it's challenging in all exercises, especially e.g. bent over rows and Romanian deadlift.