Welcome to the forums,
You can disable individual apps by visiting the COS or user features tab of your admin console GUI - via CLI it's:
su - zimbra
zmprov mc default zimbraFeatureWhateverEnabled FALSE
-For instance the Tasks tab is zimbraFeatureTasksEnabled.
-default=COSName)
Quick list:
zimbraFeatureAdvancedSearchEnabled
zimbraFeatureBriefcasesEnabled
zimbraFeatureCalendarEnabled
zimbraFeatureCalendarUpsellEnabled
zimbraFeatureChangePasswordEnabled
zimbraFeatureComposeInNewWindowEnabled
zimbraFeatureContactsEnabled
zimbraFeatureContactsUpsellEnabled
zimbraFeatureConversationsEnabled
zimbraFeatureFiltersEnabled
zimbraFeatureFlaggingEnabled
zimbraFeatureGalAutoCompleteEnabled
zimbraFeatureGalEnabled
zimbraFeatureGroupCalendarEnabled
zimbraFeatureHtmlComposeEnabled
zimbraFeatureIMEnabled
zimbraFeatureIdentitiesEnabled
zimbraFeatureImapDataSourceEnabled
zimbraFeatureInitialSearchPreferenceEnabled
zimbraFeatureInstantNotify
zimbraFeatureMailEnabled
zimbraFeatureMailForwardingEnabled
zimbraFeatureMailPollingIntervalPreferenceEnabled
zimbraFeatureMailPriorityEnabled
zimbraFeatureMailUpsellEnabled: FALSE
zimbraFeatureMobileSyncEnabled: FALSE
zimbraFeatureNewAddrBookEnabled
zimbraFeatureNewMailNotificationEnabled
zimbraFeatureNotebookEnabled
zimbraFeatureOpenMailInNewWindowEnabled
zimbraFeatureOptionsEnabled
zimbraFeatureOutOfOfficeReplyEnabled
zimbraFeaturePop3DataSourceEnabled
zimbraFeaturePortalEnabled: FALSE
zimbraFeatureSavedSearchesEnabled
zimbraFeatureSharingEnabled
zimbraFeatureShortcutAliasesEnabled
zimbraFeatureSignaturesEnabled
zimbraFeatureSkinChangeEnabled
zimbraFeatureTaggingEnabled
zimbraFeatureTasksEnabled
zimbraFeatureViewInHtmlEnabled
zimbraFeatureVoiceEnabled
zimbraFeatureVoiceUpsellEnabled
zimbraFeatureZimbraAssistantEnabled
Downsides:
In 5.0.6
Bug 28358 - UI is blank when mail feature is disabled (planned to be fixed for 5.0.7)
If you're not using mail it's one more step to mount shared items as there won't be an accept share button just above the share notice emails. You can use 'link to shared item' or createMountpoint zmmailbox/soap instead.