There is only one main difference between PKCS#5 and PKCS#7 padding is the block size. PKCS#5 padding is only defined for 8-byte block sizes. PKCS#7 padding would work for any block size from 2 to 255 bytes.
This is the definition of PKCS#5 padding (6.2):
The padding string PS shall consist of 8 - (||M|| mod 8) octets all
having value 8 - (||M|| mod 8).
PKCS#7 is the same except that it allows block sizes up to 256 bytes in size (10.3 note 2):
For such algorithms, the method shall be to pad the input at the
trailing end with k - (l mod k) octets all having value k -
(l mod k), where l is the length of the input.
So fundamentally PKCS#5 padding is a subset of PKCS#7 padding for 8 byte block sizes. Hence, PKCS#5 padding can not be used for AES. PKCS#5 padding was only defined with (triple) DES operation in mind.
Most cryptographic libraries use either PKCS#5 or PKCS#7 to define the same padding mechanism. Officially PKCS#7 would of course be the only correct one if block sizes other than 8 are used within the calculation.
Note that both PKCS#5 and PKCS#7 are not standards for padding mechanisms. The padding part is only a small subset of the defined functionality (password based encryption or PBE, and the cryptograpic message syntax or CMS respectively).