19 out of 24 words of BIP39 passphrase (brute-force last 5?) I have managed to lose 5 words of my 24 word Ledger Nano S recovery phrase. I have words 1-19 but I am missing words 20-24.
I have significant holdings on the wallet so would very much like to recover it if possible.
The passphrase is a BIP39 mnemonic (see https://github.com/bitcoin/bips/blob/master/bip-0039.mediawiki).
I have the bitcoin and ethereum public addresses for this mnemonic. I am wondering if it's feasible to brute force the passphrase.

Each word is 11 bits (2^11 = 2048 possible words).
The last (24th) word of the passphrase is of the following form [3 random bits][8 bit checksum].
Therefore I only have to check 2^(55 - 8) = 2^47 = 1.4x10^14 combinations.
I would have to compute SHA-512-HMAC with an iteration count of 2048.
As far as I understand, that means I'd have to compute 1.4*10^14 * 2048 = 2.87*10^17 hashes in total.

Is there any hardware out there designed for this? I am aware of ASICs that compute sha-256 hashes but not sha-512 hashes.
Perhaps I could tweak one to work with sha-512 since they are very similar.

Assuming a fairly typical ASIC hashrate of 1TH/s (10^12 hashes per second), I could exhaust the search space in 2.87*10^5 = 287000 seconds = 3.3 days. I'd probably get there sooner, of course (expected 1.65 days). Time is not something I am worried about. Even if I have to wait months, I don't mind - so if I can get 10GH/s at a reasonable price, that would be great.

I would really appreciate any help/information you could provide to help me out and make sure I haven't missed anything.
I could also use GPUs for this (I calculate I can run them at roughly \$1 / 10TH - so it would cost me \$28.7k to exhaust the search space, which I will do if there are no cheaper options).

Many thanks,
James
When you say that you have lost the last 5 words, are they completely gone or just difficult to read or invalid?

If you use a 48 vCPU Linode VPN, you can use BTCRecover can be used to recover 3 completely missing words in 6 hours, 4 missing words in about a 1.5 years. 24th word is actually just a checksum, so it isn't really missing...

I have a YouTube video on how to use BTCRecover and will be releasing one in the future that looks at the limits for 3-4 missing words, etc.

BTCRecover doesn't currently support using a GPU, but if that were implemented, that could easily speed things up by a factor of 10 and bring a 4 word recovery into a manageable time frame. 

Either way moore's law in on your side, so you may just have an enforced 10 year HODL. Don't throw out the 24 word seed and keep the public addresses and their derivation paths that you know about. (keeping an xpub for a known account is even better)