I feel like you're overthinking this. If the track two matches the riff, what's the problem? You're wondering how to match the tempo, but the thing is, if you're working under a daw and played your track 1 (I suspect that's the base for this whole thing) with a click, the tempo's there. The click matches the project tempo, and all midi files are configured to work under that same tempo.

It seems like you're working with a longer time signature than 4/4 judging by the second track. If you don't already know the signature and the base of your project (the riff?) is played "by feel", you can easily get the signature by recognizing a "loop"able timeframe, counting the hits and fitting it with different length notes according to your need. By all means, it can be 300483/4 if you want. If it makes it easier, make the whole project a single bar, or at least think of it like that. Then you don't have to think about any artificial boundaries or limits and can focus on what sounds right. You are the one in charge, it's your music, go with whatever feels right. (the same road goes the other way also: if it feels more natural to you, just use the 4/4 and ignore the bar lines alltogether. Might be a mess, but it'd be your mess.)

Tldr; if the second track sounds right, go with that. If you can't already figure out the time signature, then you don't either even need it or you're working on an insanely complex contemporary piece that is probably anyway better described under other rules and measures.

Sorry if I'm not being helpful, but I truly feel like you're overthinking that. And in all honesty, your post feels a little confusing to me and I probably didn't even get your point.

And sorry if my words are wrong, english isn't my first language and I bet there's a million mix-ups with my self-figured translations.

E: also if you provided a sound sample then maybe we could get you the sign. Judging only based on the image you provided it does look like 5/4 as you mentioned, but your pic doesn't really show much.

E2: actually what the heck, I might just make this easy to you. Just count the beats between the hi-hat hits that are aligned with the grid and that might just be your signature. Every beat in a daw is normally a 4th. So if you count 5 beats of 4ths, that's 5/4.

E3: Bleh I hope I'm not wrong here, thinking about this. At least most daws use the grid zoomed-in as to show a single beat or hit or whatever's the proper english word.