Another Arduino would certainly do it but it will be additional cost. I am more inclined toward using just one. I need to look more into SPI to Parallel solutions. Thanks for mentioning it.
At 5MHz SPI, ADXL375's access time is 170 micro seconds. I found out via experimenting that it totally depends on the sensor, a Bosh sensor that I had, had access time in milliseconds.
For 1 K samples/second, I have only 1 millisecond to get data from all the 5 sensors and process it, which seems really difficult; considering that I am spending about 850 micro seconds in just polling data.
If I can reduce this added up access time somehow, it will be great.