CFA / SEM handles nesting of responses within items the same way it handles nesting of repeated measures within subjects in a latent growth model: by putting the different responses into wide format (dim_a_item1, dim_a_item2, etc.). You would of course need a lot more subjects for a model with 5*10 = 50 variables, but that is just how CFA works. The "nesting" issue then disappears because all responses for a subject are within a single row, and dependence among them is accounted for in the model's covariance structure.
In this case, you would want to read about bifactor or multitrait-multimethod (MTMM) models. You would have a factor for each dimension ("trait factors"), and if the 10 items are indeed matched across dimensions (e.g., they use similar wordings or themes), then you would also have "method factors" (one factor onto which each "item1" loads, another onto which each "item2" loads, etc.). Once the trait and method factors are all specified, then you can specify any higher-order factor structure you like among the 5 dimensions. However, MTMM models are notorious for not converging, so good luck.
No, lavaan can only handle a single cluster variable.
Terrence D. Jorgensen
Assistant Professor, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam