I’d do this:
- id: TurnOnTPL
alias: 'Turn On TPL'
initial_state: 'on'
trigger:
- platform: time
at: '05:25:00'
- platform: time
at: '06:30:00'
condition:
condition: or
conditions:
- condition: template
value_template: "{{ now().strftime('%H:%M') == '05:25' and now().weekday() < 5 }}"
- condition: template
value_template: "{{ now().strftime('%H:%M') == '06:30' and now().weekday() > 4 }}"
action:
service: homeassistant.turn_on
entity_id: group.tpl