Choose the places in the password for the 2 digits to occur
in 5C2 = 10 ways.  They are

DDLLL, DLDLL, DLLDL, DLLLD, LDDLL, 
LDLDL, LDLLD, LLDDL, LLDLD, LLLDD.

where D stands for a digit and L stands for a letter.

For each of these 10 ways, there are 10 ways to choose the
first digit in the password.  That's 10*10 = 100
ways to pick the form and the first digit in the
password.

For each of these 100 ways, there are 9 ways left to choose 
the second digit in the password.  That's 100*9 = 900 ways 
to pick the form and the first and second digits in the 
password.

For each of these 900 ways, there are 26 ways to choose the
letter that comes first in the password.  That's 900*26 = 
23400 ways to pick the form, the two digits and the first
letters in the password.

For each of these 23400 ways, there are 25 ways left to choose 
the second letter in the password.  That's 23400*25 = 585000 
ways to pick the form, the two digits and the first two
letters in the password.

For each of these 585000 ways, there are 24 ways left to choose 
the third letter in the password.  That's 585000*24 = 14040000 
ways to pick the form, the two digits and the 3 letters in the 
password.

Answer 14040000.

Edwin