Have multiple email a/cs' but apple mail sending all gmail emails from same account

I have 3 gmail accounts and 2 pop3 a/cs' ( that are piggy backed by the isp to web based/imap email servers) and using Apple Mail.
Emails are correctly received into the correct email address inbox.
However, when I send an email and despite whichever email address I select in the ' From ' box on the Compose page, the emails are always sent from the same email address. This issue only affects the 3 gmail accounts, the other 2 are working ok.
In Mail Prefs I have checked that the box " send new messages from " is marked " account of selected mailbox ".
If I use gmail ' direct ' ( not via apple mail ) emails are sent from the correct account as I obviously have to sign into that particular account.
It's as if I have a default email account from which all emails are sent but the settings seem to be to the contrary.
Appreciative for any help and guidance.

Solved issue by removing the gmail accounts and then reinstating them but giving the name assigned to the server in the description field, the same as the account name ie Gmail followed by email account name ( Mail Prefs > Account Information > Edit SMTP Server List then enter in description field accordingly ).
Though you did'nt actually provide an answer you nevertheless caused me to think further for which I thank you.

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