Assistance with IF formula

Feel like I'm almost there, but seeking assistance. In one column I have 10 digit numbers, in another column, if the 10 digit number starts with 404, I want to strip the first 5 digits and return the 5 digit number; however, if the 10 digit number starts with 478, I want to strip the first 6 digits and return the 4 digit number. Below is what I have currently, please provide feedback on what I'm missing. The formula works for numbers beginning with 404; however, just returns FALSE for numbers beginning with 478.

=IF(ISNUMBER(SEARCH("404*",AA12)),(RIGHT(AA12,LEN(AA12)-5)),IF(ISNUMBER(SEARCH("478*",AA12)),(RIGHT(AA12,LEN(AA12)-6))))

Thank you so much for the assistance, unfortunately not quite what I'm looking for. Perhaps this will help. If cell AA12 contains 4045551212 or 4785551212, I need to populate the current cell with either 51212 (if it starts with 404) or just 1212 (if it starts with 478).

Thanks again!

I went back and formatted as numbers and tried again, works perfectly. Thank you both so much!!!!!!