You are right. If you have a look at this section of Act II, Doolittle deliberately asks for the money for the purpose of spending it all and having a grand time over the weekend. He is quite open about this, saying to Higgins "Don't you be afraid that I'll save it and spare it and live idle on it." He seems almost proud of the way that he promises that there "will not be a penny of it left by Monday." He wants the money for "one good spree." Thus it is, when Higgins offers him ten pounds instead of five, Doolittle says he couldn't possible accept it because of the way this is too big a sum and cannot be spent easily. Note what he says to justify his refusal of the greater sum of money:
Ten pounds is a lot of money: it makes a man feel prudent like; and then goodbye to happiness. You give me what I ask you, Governor: not a penny more, and not a penny less.
Above all, if there is one thing that Doolittle wants to avoid, it is feeling "prudent," which he sees as being akin to waving goodbye to happiness. Having too much money would make him think he would have to save it and that he was unable to spend it on enjoying himself. Five pounds appears to be the optimum amount to be easily wasted on a weekend of pleasure.
I figured it out. Doolittle could easily waste the five pounds without a thought or care, but with ten pounds, more responsibility would come. Doolittle does not want any responsibility so he would rather have the five pounds.