If the conviction was not drug-related, or for a crime of 'moral turpitude', your boyfriend probably stands a reasonable chance of getting a visa. 'Moral turpitude' includes all thefts but not minor assaults. (So, for example, shoplifting is moral turpitude but a nightclub fight [which didn't result in serious injury to the victim] isn't). See Wikipedia for further details of what is, and isn't 'moral turpitude':
http://en.wikipedia.org/wiki/Moral_turpitude
So, assuming that drugs and moral turpitude weren't involved, your boyfriend needs to apply to the US Embassy in London for an appointment for an interview, and to submit the visa application form together with his passport. He also needs to apply to the Association of Chief Police Officers for a copy of his record. Note that there's a $140 fee to be paid when making the interview appointment, plus a £35 fee to be paid to ACPO, plus an additional fee to be paid for the return of his passport by courier.
As long as the offence wasn't related to drugs or to moral turpitude, then the wait for an interview should be a fairly short one. (The US Embassy website currently indicates a minimum of 8 days but the waiting time can be far longer at some times of the year). The ACPO certificate can take up to 10 working days (unless a double fee is paid for express processing). After the interview routine visa applications are currently being decided in around 4 days but a criminal conviction (even without any involvement in moral turpitude or with drugs) can add a further 60 days, or longer, of additional processing time.
So, still assuming no moral turpitude (or drugs), your boyfriend should probably allow AT LEAST 3 MONTHS before booking any travel (as there's still no certainty that he'll get a visa).
If the conviction involved drugs or moral turpitude then the US Immigration and Nationality Act places an automatic lifetime bar upon him entering the USA. So, in the first instance, the US Embassy MUST refuse him a visa. (The embassy staff have no choice; it's their law). However the application can then be referred to Washington as an application for a 'waiver of permanent ineligibility'. If such a waiver is granted, the Embassy can then re-consider the visa application. The processing time in Washington is EXTREMELY lengthy; your boyfriend should allow an ABSOLUTE MINIMUM OF 5 MONTHS before booking travel but it would be more sensible to allow AT LEAST ONE YEAR. (The longest wait I've seen reported here on this website was for a guy who had two convictions for driving without insurance. He had to wait 15 MONTHS before having his visa application REFUSED).
You state that your boyfriend's criminal record is 5 years old. Although it doesn't seem to be a firm rule, I've seen it suggested that the US authorities require a minimum of 5 years to have passed FROM THE END OF ANY SENTENCE PERIOD before they'll consider approving a visa application from someone with a criminal record. So you need to count the time from the end of his prison sentence, community service order or supervision period, as appropriate.
US Embassy link:
http://london.usembassy.gov/b2.html
ACPO link:
http://www.acro.polic...0v%2017%202%20doc.pdf
Chris