If you read the RAID10 description, there is no indication that RAID10 is slower in performance than RAID 1. In fact, due to the striping capability of RAID10, you will find some higher depth queue to be faster.
As for RAID 5, it will be subjective depending on what you use. My real life encounter on certain pure H/W Raid card, RAID 5 is faster than RAID 1.
Most RAID 1 implementation only work in active/passive mode. No read or write is load-balanced against the mirrored disks. As such it is as fast or slightly slower due to latency to a single harddisk. For RAID 5, if the parity calculation is fast(either by a fast host, or an accelerated H/W chipset on H/W RAID cards), it is actually faster than RAID 1 since RAID 5 do support simultaneous READ. Write wise, it can be faster than RAID 1 since it's distributed across multiple drives.
I have tried configuring RAID 1 and RAID 10 and RAID 5 on 4 sets of WD Velociraptors on the Highpoint RocketRAID 4310 and RAID 5 gives a much better performance. One thing is HPT4310 has dedicated XOR engine from Intel.
So your mileage may differs depending on your actual storage architecture.