No. It will not fork the blockchain. All of the blocks produced after the fork are still valid under the old rules. This is part of what makes it a soft fork. It doesn't fork the blockchain like a hard fork does.
Technically this is incorrect. Blocks produced by non updated Miners will be forked if they come after 95% blocks are updated to new version. New nodes will not accept these blocks, old nodes will.
From the BIP:
Furthermore, when 950 out of the 1000 blocks preceding a block do have nVersion >= 5, nVersion < 5 blocks become invalid, and all further blocks enforce the new rules.
So if 5% of the miners don't upgrade, and produce a block (which will have nVersion<5), non-updated nodes will accept that block, but updated nodes will not. Once this happens, non-updated nodes will only accept new blocks from the 5% since the 95% will not be building off that
EDIT:
amaclin corrected me below,
no hardfork because, duh, old nodes will still see blocks from the 95% as valid, so even if they receive a 5% block first, the 95% will quickly build a longer valid chain, thus 'orphaning' this 5% block. So no fork really just orphaned/stale blocks. 5% miners will lose money though in wasted electricity and no block rewards.