Timing issues for backups during recovery Let's say we did a full database backup of the PRIMARY filegroup at 10:20 am. It finished at 10:45 am. We also took log backups every 5 minutes, hence 
10:15, 10:20, 10:25, 10:30, 10:35, 10:40, 10:45,...
Then we do a full backup for secondary filegroup at 10:50am it finishes at 11:00am.

Now I try to recover a database using full filegroup and log backups. I take the full backup of PRIMARY done at 10:15, restore with norecovery. What should I restore next? The logs until 10:45 with norecovery? then the second full backup after that all the logbackups after 11:50am  till the tail log with recovery? Is it the right way or should I do something else?

Thanks!
You should first restore your PRIMARY with norecovery, then your SECONDARY with norecovery, and then all the log backups from 10:15 till tail of the log, the last one with recovery.