The best advice is probably going to be with a tech at Tire Rack or some other tire wholesaler. They can help you select the best combination for your vehicle. They are experts in this.

The key is the center number in the numeric string 205/.65/R15. That number is the aspect ratio of tire width to tire height. As long as the aspect ratio is the same, then the tire circumference will be very close to the original (and your speedometer will read true).

However, consider a few factors before changing to wider tires.

First, will the wider tires fit under the fenders?

Second, while you may get better grip on dry roads, wet road traction may very well go down. As the contact area of a wider tire increases, the force downward per square inch goes down. In rainy conditions this may increase your chance for hydroplaning.

Third, changing tire size may require a four-wheel alignment to optimize the tire/road contact. If you do not, the tire may not sit squarely on the road and result in premature tire wear. You do not want to wear out those new expensive tires.

Fourth, there may be a slight chance you may experience some undesired effects such as tram-lining, where the tires are more prone to try to follow grooves and slight ruts in the road surface. You may find yourself having to apply constant corrections to the steering wheel as the car wants to follows these slight depressions in the surface. Further tuning of the suspension may be required.

Lastly, wider tires will increase rolling resistance (particularly if they are performance tires) and it will negatively impact your fuel mileage.