Combining Random Hashes - avoiding collisions and ensuring randomness
I'd treat your input as one 192 bit input instead of thinking about 5 separate inputs.
If you don't need security, you can always reduce the number of rounds of cryptographic primitives. If you merely need statistically random output, 20% of the usual number of rounds should be fine with many hashes.


A few suggestions:


SipHash has good performance for short inputs. It's pretty easy to implement as well.

The default version of SipHash has 2 rounds for each 64 bits of the input and 4 rounds of finalization, called SipHash-2-4. Sacrificing security you could reduce that to SipHash-1-2 or even SipHash-1-1.

I expect a cost of 200 CPU cycles using SipHash-2-4 on your 192 bit input on a modern 64 bit CPU and 100 cycles with SipHash-1-2.

A round of SipHash:

v0 += v1; v1 = ROTL(v1, 13); v1 ^= v0; v0 = ROTL(v0, 32);
v2 += v3; v3 = ROTL(v3, 16); v3 ^= v2;
v0 += v3; v3 = ROTL(v3, 21); v3 ^= v0;
v2 += v1; v1 = ROTL(v1, 17); v1 ^= v2; v2 = ROTL(v2, 32);


SipHash treats the input as a sequence 64 bit words. You can use A, BC, DE as the three inputs. SipHash as specified applies some padding at the end, which increases the effective input size.

Since you have constant length inputs, you can simply leave out the padding, so the input is only 3 words instead of 4.
Rijndael-256 truncated to 64 bits. This should have great performance when used with AES-NI, but implementing it yourself will be hard.
MD5

While it's not secure against deliberate collisions, accidental collisions are as rare as one can expect. But it will be a bit slower than the alternatives.
A variant of Skein256

Skein is fast on 64 bit CPUs. Use the variant based on Threefish256, not the variant that uses Theefish512 and merely truncates since, the smaller block size doubles performance for short messages. Remove the finalization compression, it's only necessary for some security properties you don't need.

Then you can proceed to reduce the number of rounds to the smallest value that's still random enough for your purposes.   


Personally I'd go with round reduced SipHash.