In a bid to keep up with its competitors, such as the iCloud service coming from Apple in the fall, and the Skydrive service available to Windows Phone 7 users, HTC is offering a cloud-based storage service package of its own — with the help of Dropbox.

The Taiwanese smartphone giant will be giving those who adopt its new handsets — running HTC Sense 3.5 — up to 5GB of Dropbox storage absolutely free. That includes the 2GB you already get for free from the service, with HTC covering the additional three.

The first handset to take advantage of the service is the HTC Rhyme — a handset aimed at the ladies, which will be available this October. Dropbox access on your HTC handset will allow you to store photos, music, and documents in a cloud-based locker for access from your PC and other devices connected to the same account.

It’s unclear at this point whether HTC will allow its existing customers to upgrade to Sense 3.5 — giving them the same 5GB of free Dropbox storage — or whether the offer will be extended to its Windows Phone 7 users, who already have 25GB of free storage from Microsoft’s Skydrive service.

Will you be pleased to get 5GB of Dropbox storage with your next HTC handset?