That's not what you posted in your initial post.
The clause you are citing is a typical clause and it relates to something like fire, flood damage, or severe damage to the apt. I don't think you can apply that to a roach infestation. Besides, what makes a roach infestation 2,3, 10 roaches? You need to directly contact your landlord and build a paper trail. Call code compliance if you must. If they shut him down, then you are out. But, it is more likely they will give him a notice and a deadline by which he has to eradicate the roach problem. In some cities, living with roaches is a given and there is little one can do but fight them on a daily basis.
signed a lease beginning of this month and on the lease it states if tenant can not move in within five days due to property damage. all the money will be refunded
The clause you are citing is a typical clause and it relates to something like fire, flood damage, or severe damage to the apt. I don't think you can apply that to a roach infestation. Besides, what makes a roach infestation 2,3, 10 roaches? You need to directly contact your landlord and build a paper trail. Call code compliance if you must. If they shut him down, then you are out. But, it is more likely they will give him a notice and a deadline by which he has to eradicate the roach problem. In some cities, living with roaches is a given and there is little one can do but fight them on a daily basis.