How should you incorporate strength training to improve your speed?

Again, I'm looking to get faster long-term and am currently on week 5 of C25K.

You'll be faster by next week. Repeat for months.
I'd suggest coaching if you're going down the serious route.
You're looking at intense training and intervals plus track time.

Where should I start

Wing it. Stop focusing on speed so much and get a whole canvas/foundation down before you add detail. Form. Breathing. Diet. Sleep. Stress. Life. Think about all the little gaps to fill before diverting your focus to speed or you will end up worse off.

I don't want to just wing it

Why not experiment? Screw pseudoscience. If you've not done much prior to C25K you'll still be developing absolute basics in your breathing, form, psychology and musculature well beyond W8/9 or whenever you 'graduate'. Incorporate in moderation and go by what you feel, providing you don't overdo it you'll be just dandy in your W5D3.
Fartleks are a fun way to spice up your 5k, get a map out and read contours on your local trails, get viewranger out and plot a route then check the analysis for elevation - go run some rough and ready uphill slogs come rain or shine - look at some strava segments and go time yourself on some sprint sections or stairsets for a laugh. Cross train, even if it's some angry hiking or mountain biking or even just a potter round a park.

where should I try to end up
What's the actual goal? 5k speed demon? 10k dark horse? What's your current pace time and what do you want? Long term, until you have an actual solid figure to crunch on, you're going to be killing it week on week anyway.

At this stage there's nothing wrong with building your own little ritual and I'll use mine as an example - I'll do a simple walk warmup and set off reasonably easy, seeing how I feel after hill1 before mile 2 where the long uphill starts - I'll push it on the steeps here and gun the final sharp incline before taking it easy for the rest of the next 1/2 mile into mile 3, on the final 0.6 mile after a long downhill breather it's the final uphill where IF I have the steam left, it's ALL going there followed by a 10/15 minute walk home to a stretch set with planks/pushups/squats all incorporated because I lacked strength.
I'll change the run up with long/shirt speed bursts, exaggerated and long powerful strides or throwing myself into the mud to force high legs, heavy feet and a completely different way of carrying my legs. Tried to change my run to include a different uphill that insta-killed my legs, took me from 26m to 30 - So that was strength/endurance that sent me home scheming.

I added a walk to go powering slowly and with purpose around all the trail stairsets I could find keeping my heart rate 70-80%, I then did a followup run to break out my 5k comfort speed zone and aimed for a specific hill, knowing full well it was brutal for about 2 solid miles while slithering in the mud.
I slowed down to a slow that felt horribly uncomfortable in order to stand a chance at it but having looked at the run info, my speed was actually faster than imagined (10k mark in 1:06 without pushing at all)

Source: Casual as and I know shit all and got fixated on speed on W7 when I did my first 31minute 5k, another 4 or 5 weeks later and I was running 24:10 on flat and 26 on my trails - I got so caught up on speed I went tunnel visioned and plateaud myself into mild irritation.

Being serious, gauge what you feel when you hit W5D3 - yesterdays fast is todays slow.

/r/C25K Thread