Trying to calculate the strength of a Bitcoin brain wallet created with a custom diceware password
Generally correct. 

It would take approximately 7 years to brute-force all possible keys generated by your brainwallet format, for an attacker with 1Petahash/sec hashing power. For reference, the current hash rate of the entire Bitcoin network is roughly 1 exabyte / second, 1000 times your hypothetical attacker's hash rate. 

This means that on average it would take approximately 3.5 years to crack a single brainwallet. 

You also mentioned precomputed hashes. For an attacker to precompute all of the given hashes (assuming 32 bytes per SHA256 hash), they would need to store $46656^5 * 32 \approx 7.07 * 10 ^ {24}$ bytes, amounting to 7.07 yottabytes. This is currently an unpractical amount of storage.