How do you break a tie to conduct business or vote him out when irrational president refuses to cosign POA checks and also has 5 of 10 votes and bylaws do not specify any tiebreaking rules?

Your governing documents should contain a description of board votes, including the number of votes on the board. Usually this is an odd number, not an even number. Usually, you can find these in the CC&Rs; modifications are usually contained in the by-laws. (A condominium-savvy attorney can help you understand your governing documents, including all their modifications.)

(With an odd number of votes on a board, the board votes without the president, and when necessary -- in the case of a tie -- the president's vote is the tie-breaking vote.)

Unless the president is a developer -- not an appointee of the developer -- having five votes on a board with ten votes is highly unusual. (Unless the president is in possession of four proxy votes from other board members.)

If other board members believe -- as apparently you do -- that your president is a 'rogue' board member, it is the responsibility of the board to convince the president of the gravity of the position, or vote the president off the board. (See link, below.)

In the case of not paying bills: This unreasonable behaviour can't continue for long, since vendors will not perform services, insurance will be cancelled and owners may rebel when the bills of the association are not paid.