Cant figure out my mistake with subnetting problems (CIDR notation)

I an given the network ID 172.24.72.0/23

and I'm asked what the subnet address of Subnet A is given subnet A has 24 hosts.

I know that 24 hosts plus 2 for broadcast & subnet ID is 26, and that it takes 5 bits to support this many hosts.

I also know that 32-5 will result in a 27 bit mask

This is where I think I'm screwing up...

172.24.72.0	10101100	00011000	01001000	00000000
/27 mask	11111111	11111111	11111111	11100000
AND	10101100	00011000	01001000	11100000
convert to dec	172	24	72	224

All this leads me to believe that 172.24.72.224/27 should be correct, but my answer is being rejected. after so many failed attempts, I'm given the following explanation:

Subnet A has 24 hosts, so it will need at least 26 addresses (for the subnet ID and broadcast address). The least number of bits that satisfy this is 5 bits. Knowing that, we take the prior subnet and add 32, the result of which is 172.24.72.64/27

I think the detail that I don't fully understand is the part that says, "we take the prior subnet and add 32." can anyone please hint at what I'm misunderstanding? I don't require a full solution. this is not a homework problem. it's from a bank of sample problems I'm using to study.

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