Given that the 205/55-15 tire is almost 1/2" taller in diameter overall compared to the OEM 185/65-14 tire size. There may or may not be an issue with clearance.

Wether or not you will run into clearance issues - will depend on the wheel chosen (wheel offset or backspace), suspension modifications, and which 15" tire you were thinking of getting.

If the offset of the wheel is incorrect, doesn't matter what tire you put on there, you could have a clearance issue. For the 8th generation Corolla - offsets of 38mm-45mm are supported, depending on the wheel size. Wheel widths up to 7" are supported as well, depending on the wheel offset.

Suspension mods are self explanatory - if you are running a lowered suspension or have the original one that is starting to sag, you may run into a clearance issue with a taller, wider tire.

The choice of tire can be important, as not all 205/55-15 tires are the same size. Dimensionally, they will fit a 15" wheel and have a 205mm tread width and sidewall is 55% of the treadwidth - but some tires have a larger tire carcass, their tread actually could be smaller or larger than 205mm.

Ideally, you want to run a 195/55-15 wheel to avoid or minimize any clearance issues.