so heres where i’m at:
i have enough gems to do about 3 10pulls.
my SH is at 20 and i have a TC at 16 and 2 more at 13. i estimate 3-4 weeks to finally get it trying for 5*s.
would it be better to use my gems to speed up building to get started trying for 5s via the TC? or do the 10pulls in hopes of getting a 5 and waiting to get the TC running?
Split the difference, use gems to summon troops. You’re guaranteed a return notes than feeder heros
I think it depends on your current team make-up and depth.
If you already have a solid team of 4* with some 5*, but are looking for better, you’d probably be throwing away the gems in summons. If you have 3* and some 4* then the gems are likely to give you at least a couple of improvements in your team.
Agree with @Talisax if you are at the point of diminishing return on your Hero summons, it’s worth getting more troops.
Otherwise spend on accelerating missions if you have a number of heroes still awaiting ascension and you are missing items. The faster you turn those around, the more chance of Rare missions which are likely to net you rare ascension materials.
so i have a solid stable of 4* heroes. at least 2 good ones in each color. sadly despite my many attempts at 10pulls, this game has deprived me of a 5*. (its weird, i’ve never had a “bad” 10pull. they’ve always had some good 4s but 5s elude me at every opportunity)
as for troops, i have 3 colors of 4* troops, still missing red and green. but otherwise i’ve got them well rounded.
i’m mostly unsure if its worth doing the 10pulls considering my luck thus far (though i feel like i’m finally due something!) of if i’d end up with a better chance at a 5* from the TC’s starting sooner.
honestly though, if i were going to do 10 pulls, i’d probably wait til next month’s event anyway, so this may be a moot point.
Summoning troops is about getting good feeders as well as rounding our 4*
are you meaning summoning random heroes or troops? the terminology can sometimes get confusing.
my main team is all at 4/70 and backups are all at or close to 3/60. i have some ascension mats to raise them but haven’t done so yet in case i get something better.
I am meaning troops. It takes a gazillion troops give or take
Depend how your ascension materials are looking like, no point having a 5 star sitting at 2/60 or even 3/70. If they’re looking good try summoning
As for building; I’ve thought about speeding up but if the trainings take 2 days and it usually takes people 10 tries to get a legendary, that’s 20 days for you to do whatever you want and I think you would regret spending gems
if you use summons for troops, you have zero chance at hotm. something to consider.
Same here, go for a HotM first.
Then you can save the rest for the next month or use what you spare (if you spare something) for whatever you want.
Unless you’re a regular spender with a budget for this, there’s 3 things worth using gems on: A few expansions of hero storage, shortcutting wanted-chests and hero summons.
Skipping build times in a slow paced game like this is definitely the least sane way to waste your gems. Troops come second. However, if you have the will and ability to spend generously, by all means keep at it! 
He can do only 3 x 10 pulls. He may be lucky, but for example I got Zeline after 9 x 10 pulls…
It’s more than 10 tries in TC 20 for most people. I’ve done 70 legendary trainings and only have 1 5* and it was at pull 53!
Currently I’m no 5* for 32, and just got my 18th 3* in succession. Assuming the calculated averages of TC20 results on this board are accurate, there’s roughly a 1 in 200 chance of that streak happening.
But spending for heroes summon is the only way to get it.
A small chance is better then none.