lil nicki,
Personally, I like your shoes. I have been running for years and have worn Brooks, Nike, Adidas, Puma, Reebock, etc. I recently become an Asics fan. I got turned on to them in January by a store clerk who just graduated from Drake, where he was on the track team. He said all the men there were wearing them. I have a pair of the Nimbus and a pair of the Kayano. The Kayano has more arch support which helps if you tend to pronate in, like most runners. I like the Asics better than any shoe I've tested, because it gives me a smooth ride, plenty of cushioning, no blisters, it doesn't weigh too much, and it wears very well. I finally found a running shoe store that can do a proper gait analysis, and it turns out I do not pronate, so I can use a "neutral" shoe. So I switched to the Nimbus, which is the best shoe I've ever had for my feet. Everybody's different, though, so you have to try on other shoes until you are satisfied that you have the best shoe for you. The good running stores will let you run on an in-store treadmill, or even take them for a test drive around the block.
As far as your training schedule goes, I would say that it's fine, provided you aren't picking up recurring injuries from the stress of running. 35-40 miles per week is more than enough to prepare you for a half marathon. It's enough for a 25 or 30K, actually. Since you are interested in improving your
PR in the 5K distance, I would focus more on quality runs and maybe cut back the overall mileage. Try some hill repeats and quarter mile repeats, 600 meter repeats and tempo runs, where you ratchet up the tempo in steps and then gradually decrease the tempo back to where you started. You mustn't do the quality runs all the time, because you will injure yourself. I suggest alternating between these intense workouts and your longer, slower runs. In fact, one or two quality workouts per week is enough. Your weekly mileage will decrease, but your overall fitness level and top end speed will increase. I guarantee it.
Your idea about weight lifting is good. I do a lot of cross training, because I do triathlons. I lift 2 times per week during the race season and 3 times per week in the off season. As a runner, your goal is not to pack on slabs of muscle. You want a strong core and lean upper body to enhance your overall conditioning and eliminate upper body fat, which is just excess weight for a runner. If you do squats, leg presses, or leg curls, go for lighter weight and more reps. You're looking for endurance muscles, not the fast twitch muscles that give football and soccer players their explosive speed. Because I do a lot of biking in addition to running, supplemented by yoga and core classes that include a lot of lunges, I no longer do weight training for my legs. But I am strengthening the stabilizing muscles with those other activities.
Swimming is a great non-impact alternative if you want a cardio work out and you're too beat up from running.
Active.com, Activetriathlete, and halhigdon.com are all great on-line resources for runners and they're free.
Best of luck with your training. I commend you for the interest you are taking in your health and your body. Keep up the good work.