If you mean that you want to use the same keyword for a different site, than its fine. You might wanna specify your question. What is the method, is this involving linkwheel, etc

I'm outsourcing my backlinks and they're asking me to provide 3 keywords and 5 urls

My 5 urls consist of my moneysite homepage, internal pages on the moneysite and some articles with links to the moneysite.

Is there a problem with using just one keyword to point to each of the url's?

There's only one keyword I'm really interested in ranking for, but everyone says to choose several, low competition, long tail keywords. I want to know the downside to ignoring all other keywords and targeting just a single, high traffic keyword (other than it possibly being difficult to compete for).

Will I lose link juice or something similar because my one keyword is plastered on all of my backlinks?

No there isn't - but I would seriously think about using at least two KWs unless your single KW isn't that competitive.