I want to synthesize methyl 3,5-dibromobenzoate (3,5-dibromobenzoic acid methyl ester).

This can be synthesized from the corresponding benzoic acid, ester, or aldehyde, which are all meta- directing. However, they strongly deactivate the benzene ring and make bromination difficult. Even if the first bromination is achievable, i cannot find any papers on how to do the second one.

I don't have access to an already bromo- substituted benzene compound.

Is there an easier synthetic route? I am struggling in finding any papers for reference. 

I am very new to Organic Chemistry and although it seems like an easy target I still find it extremely difficult.

Some targets look deceptively easy just because they're small. You received some synthetic advice over on Chemical Forums that looks good, so I won't bother too much with that. I would add a small word of caution that sometime you end up sinking more time and money into making a target than what you would have spent if you just bought it. This compound is commercially available and quite cheap. Alfa sells 5 g for a bit over $23. I don't know where you are based or what resources you have access to, but were I your position, I would just order it. 

12 hours ago, hypervalent_iodine said:

Some targets look deceptively easy just because they're small. You received some synthetic advice over on Chemical Forums that looks good, so I won't bother too much with that. I would add a small word of caution that sometime you end up sinking more time and money into making a target than what you would have spent if you just bought it. This compound is commercially available and quite cheap. Alfa sells 5 g for a bit over $23. I don't know where you are based or what resources you have access to, but were I your position, I would just order it. 

Thanks for the advice!