First up: a 5 bit LFSR is horribly small, so getting the initial seed which was used is a piece of cake.
But indeed, it’ll basically boil down to a (rather quick) brute-force job where – unless that file contained purely random data – you’ld have good chances detecting the initial state (resulting in successful decryption) by just looking at the first couple of bytes.
Remember executable files, images, compressed files, and specific program files (like MS Word files) all come with specific headers. And text files can easily be detected too. UTF-8, UTF-16, etc mostly include BOMs (Byte Order Marks) and even if they don’t, they’re text – which greatly differs from random binary data. This makes "attacking" easier and can speed up things in scenarios where you’re facing multiple encrypted files each using different seeds.
That being said – never, ever, use a plain LFSR for encryption. If you really need speed, use a stream cipher (and don’t forget to use a MAC for authentication, as in "encrypt-then-MAC").