I assume you're referring to 5 turn-based games at the same time? Because I've just checked their profile and it seems to be the case.
Turn based games are games with much longer time formats, meaning that you don't have to, or aren't obligated to, make a move asap..
Now there's the thing, most turn-based games have their moves played at the rate of like 1-2 moves a day. So, it is probably not the case that your opponent was pre-occupied with 5 games at the same time. In fact, there are people who have like 80+ turn-based games at once, and still play live games. I have 10 games turn-based, yet the vast majority of the time, I have no moves to make there. So I play a bunch of live.
In fact, having 5 turn-based games at once, is too small a number.
It is impossible on bga to play more than one live game at once.
The reason for your opponent's "slow-moving" could also be due to thinking as Targi is a game that requires thinking ahead a lot of the time, and denying opponents. It seems like your opponent is a high-rated player, so that would make some sense as high-rated player see more to the game and have more details to keep track of.
Nevertheless, if you don't enjoy waiting "forever" for opponents to make a move, you could try:
1. Asking them to go faster
2. Play at 'fast' time format, instead of 'normal'
3. You could even try multi-tasking a little bit. It can be helpful in some games that are by nature slow. and doesn't require your attention the whole time.
