The FA's rule that covers this:
7. PUNISHMENTS – Relating to First Team Competitive Matches
(a) CAUTIONS ADMINISTERED ON THE FIELD OF PLAY
(i) If a Player accumulates five recorded cautions in FTCM between the opening day of the Playing Season and the last day in February in the same Season, he will be suspended automatically for a period covering: -
One First Team Match
(ii) If a Player accumulates five recorded cautions in FTCM between the opening day of the Playing Season and the last day of the same Season, he will be: - “Warned as to his Future Conduct”
(iii) A Player who has already been subject to disciplinary action as a result of recording five cautions and then proceeds to record a further five cautions during the same Season, will be subject to the following punishments: -
(iv) If a Player accumulates ten recorded cautions in FTCM between the opening day of the Playing Season and the second Sunday of April in the same Season, he will be suspended automatically for a period covering:-
Two First Team matches
(v) If a Player accumulates ten recorded cautions in FTCM between the opening day of the Playing Season and the last day of the same Season, he will be: - “Severely Censured and Warned as to his future Conduct”
(vi) If a Player accumulates 15 recorded cautions in FTCM between the opening date of the Playing Season and the last day of the same Season, he will be suspended automatically for a period covering: - Three First Team matches
(vii) A Player who has already been subject to disciplinary action as a result of recording five, ten and 15 cautions, and who goes on to record 20 cautions in FTCM in the same Season, shall be required to attend a meeting of a Disciplinary Commission, within seven days of the date of the last caution. The Members of a Commission will have the power to deal with the Player in such manner as they deem fit. The same procedure will apply for every further five cautions recorded against that Player.
(viii) Any period of suspension arising from recording cautions will commence on the seventh day following the date of his last offence. The suspension will cover all approved First Team matches until such time as his Club’s First Team has completed the number of matches appropriate to the punishment in approved Competitions during the period covered by its opening league match and ending with the final match in which the Club is playing in an approved domestic Competition.
(ix) Any period of suspension or part thereof which remains outstanding at the end of a Season must be served at the commencement of the next following Season.