Which reaction occurs first when 5-hexen-1-ol reacts with sulfuric acid? I am trying to solve this question:

Find the major product of the following reaction:


Now we could either do electrophilic addition on the alkene or do dehydration of alcohol. These two different reaction pathways yield different products. So how do we decide which reaction occurs first?
I thought that electrophilic addition could be favored because of the generation of a carbocation that could then undergo $\mathrm{S_Ni}$ reaction with the $\ce{-OH}$ generating a cyclic structure. Now if the cyclic structure were more stable than the open chain product formed by dehydration of alcohol then this reaction could be favored. But I don't know how this could be proven.
In general, intramolecular reactions occur faster than their intermolecular counterparts. Most commonly this is rationalized by an entropic argument: in the case of the intermolecular reaction, two molecules (substrate + water) combine to form one (diol). This is entropically disfavored relative to the intramolecular case, in which the molecule cyclizes.

However, the biggest factor at play in determining which will occur in this case is the size of the resulting ring. If the product contains a 5, 6, or 7-membered ring, these rings are considered be unstrained (bond angles ~ 109.5 degrees). If the rings are smaller than 5 atoms or larger than 8, the rule of thumb is that the thermodynamic (enthalpic) cost of the ring strain associated with cyclization overcomes the entropic driving force to cyclize, and the intermolecular reaction is preferred.