Yes.
View all private messages and you'll see " Show Messages From ..." the default is five days. Change it via the pull down menu to the "the beginning" option, to be able to delete the older messages which are filling up your inbox but which don't show by default.
Then, also at the top is the " Jump to folder" option. You can then change to 'Sent Items' and again, view from the beginning and delete any older messages you don't want to save there too.
That should free up the space for your Inbox.
-decadence
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