Let me start by saying I've had trouble with 13's in the past. Maybe it's my lack of complete tuning virtuosity but I don't think so. I just can't seem to get along with 13's try as I might. 10" drums are hard to make sound bad!. OK...im at rehearsal one afternoon using our bass players sons kit which was a Mapex set with an 11x13 and is the first 13 out of God knows how many that sounded better than good. I've been hooked on 11x13's ever since. So definitely rock the world with your 10 and 13.
Size wise anything goes tonally. Fit wise, that depends. Not a chance I could fit the 13 over my 22” BD as a traditional 5pc setup and be comfortable, but if it works for you, go for it. If the 13 fits fine, I’d go for a 12 instead of 10. A 12 will tune up to a 10 and have volume like the 13, but a 10 will never tune down to a 12 effectively and volume will never match. I’m assuming with those sizes you want low toms. None of my 10s have ever liked low tuning.
Preface: I'm not a huge fan of 5pc set ups or 10" or 13" toms so take this all with a grain of salt.
With that said: If I had 10" and 13" mounted toms with an 18" floor tom I would use the 13" and the 18" in a 4pc set up style (the tonal 'jump' from 10 to 18 would sound weird, in my opinion) then use the 10 somewhere else for some added flavor. Maybe mounted after the floor tom, this could allow you to add some tonal 'pop' to the end of a fill. Maybe mounted in the side snare position opposite your hats to give you some left hand flexibility fill/accent wise. Maybe mounted in between the 13 and 18 in a 5pc configuration so it's there if you want it BUT you are not always jumping from 10 to 18 tonally.
Now, if it were actually me in this case.... I would convert the 18 to a bass drum then use the 10 and 13s as toms in a 4pc set up and sell my other bass drum because I'm tired of lugging large drums around but I don't believe that matches your intention here haha.
go for it! ive played a 10/13/16 and 10/13/18 before now and it works sonically!
as long as you can get them in a position you feel comfy in, then it'll work for you. ive currently got a 12x9 and 14x11 as my rack toms, and an 18" floor tom with a 22x18 bass drum, and it works great! give your setup a try, see if you can position them in a way you feel comfy, then roll with it
I had a 10/13/16, roughly the 13 was a 5th apart with the 10/16 an octave. It worked but it is a jump and I didn't always like it. I prefer 10/12/14 which I can easily add up or down (8 or 16) and have tuning range that can flex alot better as a group.
I'm done with 13" toms. I've had a couple and was constantly messing around with keeping them in tune. I can't think of any company that doesn't make a good sounding 12". Why bother with a 13? You'd be better served with a square sized 14x14 FT. If you're going 5 pc 2 up, 1 down, stay with 10-12-16. 18" FT's are generally no bargain to keep in tune either. But in the end, your call. Only you know what works for you. As far as resale goes 22-10-12-16 is about the easiest to sell from my experience.
A 12"x8" in a snare stand is the only rack tom for me. No other size appeals. It presents a great contrast with a 16"x16", the only floor tom I play, and it doesn't consume inordinate space. It's there's one thing I never think about, it's changing my tom configurations.